By MICHAEL FALCONE ( @michaelpfalcone ) and AMY WALTER ( @amyewalter )

NOTABLES:

• FISCAL-CLIFF LATEST - THEY'RE GETTING CLOSER: With a new proposal from the White House Monday night, sides appear to be moving a bit closer to agreement. ABC's Jonathan Karl reported that the White House presented a new offer to Speaker of the House John Boehner that makes some important concessions. This comes in response to the offer Boehner made to allow tax rates rise on those making $1 million. The new offer from the White House includes fewer tax increases and more limits on entitlement spending (including limits on cost of living adjustments for Social Security recipients) than the President's previous offers. Speaker of the House John Boehner will present this latest White House offer to House Republicans today. http://abcn.ws/U5r7qM

• HOW THE WHITE HOUSE IS CASTING IT: ABC's Jake Tapper reports on how the White House explained the deal: "The President's counter-offer to Speaker Boehner presented today included the below. You shouldn't cast this as our final offer, but we view this as a good offer that shows we have met the Republicans more than halfway on spending and halfway on revenues. Even after the over $1 trillion in cuts in the [Budget Control Act], this offer reflects a dollar in spending cuts for every dollar in revenue. The deficit reduction below amounts to 2.4 trillion; when added to the 1.1 trillion in spending cuts in the [Budget Control Act] plus savings from [Overseas Contingency, aka foreign wars] achieves over 4 trillion in deficit reduction."

• KEY CONCESSIONS FROM OBAMA: Karl and Tapper report that key concessions include $1.2 trillion in tax increases, instead of $1.6 trillion; extending the Bush tax cuts for everyone earning under $400,000 (the previous White House offer was $250,000); adjusting the way cost of living is adjusted, resulting in lower annual increases for Social Security recipients, except for the neediest; $1.22 trillion in spending cuts; and a two-year extension of the debt ceiling. http://abcn.ws/U5r7qM

• FROM THE SPEAKER'S DESK - A STEP, BUT NOT BALANCED: Reaction from Boehner spokesman Michael Steel: "Any movement away from the unrealistic offers the president has made previously is a step in the right direction, but a proposal that includes $1.3 trillion in revenue for only $930 billion in spending cuts cannot be considered balanced," Steel said. "We hope to continue discussions with the president so we can reach an agreement that is truly balanced and begins to solve our spending problem." In other words, this won't be the deal, but it is considerably closer than where we were last week. http://abcn.ws/U5r7qM

THE NOTE:

It was an eerie coincidence of timing that yesterday turned out to be a history-making moment for the U.S. Senate.

In the space of less than 24 hours the upper chamber lost its longest-serving sitting member and the second-longest serving senator in U.S. history with the death of Hawaii's Daniel Inouye.

But just hours earlier, the Senate became poised to gain its first African-American member from the South in more than a century with South Carolina Gov. Nikki Haley's appointment of Congressman Tim Scott to succeed stalwart conservative Sen. Jim DeMint.

And with President Obama's intention to nominate Sen. John Kerry to be the next Secretary of State, the Senate will soon lose one of its leading foreign policy voices with an interim appointment followed by a special election in Massachusetts looming on the horizon.

The passing of Inouye, who represented Hawaii in Congress since it became a state in 1959, triggers up a two-step succession process. First, the Hawaii Democratic Party must submit three names (all must be Democrats) to Gov. Neil Abercrombie, who will then select one from that list to be the next senator.

And Inouye, himself, may have some influence on that decision.

The late senator's office said that it was the 88-year-old Democrat's dying wish for Congresswoman Colleen Hanabusa to replace him. According to Inouye's spokesman, the senator wrote a letter to Gov. Abercrombie before he died asking him to appoint the congresswoman, elected to the Hawaii's 1st Congressional district in 2010, to fill his seat.

That request virtually guarantees that Hanabusa will be among the three names submitted by state Democrats to the governor and knowledgeable Hawaii Democrats say it is likely to weigh heavily on his decision.

With the death of Inouye and the departure of Sen. Daniel Akaka in the New Year, the 50th state is losing virtually all of its seniority. Hawaii Democratic state Rep. Angus McKelvey, whose family has known Inouye for years and who calls the late senator "Uncle Dan," told The Note that the governor would be smart to appoint someone young enough to begin to rebuild that seniority.

"Hawaiians," McKelvey said, "understand that small states have to have elected officials with longevity."

NOTE IT!

ABC'S RICK KLEIN: Perhaps it took a clarifying moment - a tragedy involving children - to make everyone start acting like grownups. Both sides in the fiscal cliff debate are now trading serious proposals, and the biggest disagreements left revolve around numbers more than policy options. That makes an agreement likely, it not quite easy. If any deal is to collapse, today may be the most important day on the cliff calendar, as House Speaker John Boehner briefs his conference on the status of negotiations. We haven't seen hard-liners on the right rise up in protest over the direction Boehner is taking his party; if that doesn't happen today, it looks like clear sailing, relatively speaking.

POLL: OBAMA WELL POSITIONED ON CLIFF, BUT NO MANDATE. The president enjoys solid job-approval numbers as the fiscal-cliff fight rages, but Americans don't see an electoral mandate, ABC's Gary Langer reports on the latest ABC/Washington Post poll: His job approval rating, at 54 percent, is his highest (excepting a brief bin Laden bounce) in nearly two years. And even while weakly rated on the economy, he leads the Republicans in trust to handle it by 18 percentage points, his widest margin since July 2009. But for all his advantages, Americans by a wide 22-point margin, 56-34 percent, say Obama does not have "a mandate to carry out the agenda he presented during the presidential campaign," but rather should "compromise on things the Republicans strongly oppose," a sign of risk for the president if the talks should collapse. http://abcn.ws/TXx8TY

THE BUZZ:

with ABC's Chris Good ( @c_good)

OBAMA PLEDGES ACTION ON GUNS, BUT WHAT? Reporting for "World News," ABC's Jake Tapper notes the President Obama has pledged action on guns, but the White House hasn't offered any specific proposals in the last four years. Proposals in Congress include reinstating the assault weapons ban and prohibiting high-capacity magazines. http://abcn.ws/V4PxS5

REMEMBERING SEN. INOUYE. ABC's Sunlen Miller reports: Sen. Daniel Inouye, the 88-year-old Democrat who has been in office since Hawaii became a state in 1959, has died. His last word was, "Aloha." He became Hawaii's senator in 1962, three years after the state joined the United States. He was the longest serving sitting Senator and the second-longest serving senator in U.S. history. … A decorated war hero who lost his arm in battle, in 2000 Inouye was awarded the Medal of Honor for his service in Europe in World War II. He was a champion for veterans and veterans rights. On Capitol Hill he rose to become Chairman of the Senate Appropriations Committee, which controls the purse strings for the nation and is widely considered one of the most powerful positions in government. He worked hard to bring federal dollars, particularly from the military, to his island state. http://abcn.ws/R2tWsS

OBAMA ON INOUYE: A 'TRUE AMERICAN HERO.' ABC's Jake Tapper reports on the president's statement in response to Sen. Inouye's passing: "Tonight, our country has lost a true American hero with the passing of Senator Daniel Inouye. The second-longest serving Senator in the history of the chamber, Danny represented the people of Hawaii in Congress from the moment they joined the Union. In Washington, he worked to strengthen our military, forge bipartisan consensus, and hold those of us in government accountable to the people we were elected to serve. But it was his incredible bravery during World War II-including one heroic effort that cost him his arm but earned him the Medal of Honor-that made Danny not just a colleague and a mentor, but someone revered by all of us lucky enough to know him. Our thoughts and prayers are with the Inouye family.

BIDEN ON INOUYE: 'COURAGE PERSONIFIED.' Both the president and vice president served alongside Sen. Daniel Inouye in the Senate Democratic caucus, and ABC's Arlette Saenz reports that Biden released this statement: "As my mother would say, the greatest virtue of all is courage, and Danny was courage personified. From the battlefields of World War II where he received the Medal of Honor, to the floor of the United States Senate where he displayed incredible moral bravery, he was always the same - courageous and resolute. He was one of the most honorable men I ever met in my life, and one of the best friends you could hope for. He was honest, and fiercely loyal, and I trusted him absolutely. Everyone in the Senate not only admired Danny Inouye, but they trusted him. We all knew he would do the moral thing regardless of the consequences-whether it was passing judgment on a President during Watergate or on another President in the Iran Contra hearings. …"

CONSERVATIVE FLAK FOR BOEHNER. After reports over the weekend that House Speaker John Boehner had offered to put the one-year debt-limit increase on the table, the conservative Club for Growth blasted him for it. Huffington Post's Sabrina Siddiqui reports: "'First Speaker Boehner offered to raise tax rates after promising not to, and now he's offering to raise the debt ceiling. Raising tax rates is anti-growth, and raising the debt ceiling is pro-government growth - and this is the Republican position?' said Club for Growth President Chris Chocola in a statement issued on Monday. 'Raising the debt ceiling would give away one of the best tools the Republicans have in their arsenal to force real reform.'" http://huff.to/T5AuH6

PROTESTERS OUTSIDE THE NRA. ABC's Sarah Parnass and Arlette Saenz report: Chanting "Shame on the NRA," a couple hundred activists marched Monday from a park on Capitol Hill to the NRA's office. A nonprofit group called CREDO Mobile organized the "emergency march" in the wake of the killing of 20 children and six adults Friday at Sandy Hook Elementary School and suggested that the NRA contributed to the gruesome murder through the policies it promotes. Holding a sign reading, "I'm a victim of gun violence," Eddie Weingart, a massage therapist from Silver Spring, Md., recounted how his mother was shot and murdered by her ex-husband, who also tried to shoot him when he was just 2 years old. http://abcn.ws/YfWDWH

HOUSE HOLDS MOMENT OF SILENCE FOR SANDY HOOK. ABC's John Parkinson reports: The House of Representatives observed a moment of silence Monday evening to honor the victims of the Sandy Hook Elementary School shooting in Newton, Connecticut last Friday. Connecticut Democratic Rep. Chris Murphy, whose congressional district includes Newtown, joined House Speaker John Boehner to lead the chamber in the somber tribute at 7:05 p.m. "When you peak through this vast crippling darkness of the last four days, there's one answer that we know for certain: If we ever wondered what kind of community Newtown was-if we ever doubted the deepness of our love for one another-those question have been answered. They've been answered definitively," Murphy said. "Newtown is going to survive this because it's a close town, and they hurt more because they're close, but they also can survive because they're closer. They can also survive because they just will get this inspiration-these 20 little kids, who just are asking this town to remember how good they were and to try to equal it."

ASSAULT WEAPONS BAN: WHAT WAS IT, AND DID IT WORK? ABC's Elizabeth Hartfield reports: While new legislation likely won't be introduced until after Jan. 3, statements from top Senators such as Dianne Feinstein (D-Calif.) and Frank Lautenberg (D-N.J.) suggest that new proposals could be similar to the Federal Assault Weapons Ban that was in in place from 1994 to 2004. … Passed by Congress on Sept. 13, 1994, and signed by Bill Clinton later that day, the Federal Assault Weapons Ban prohibited the manufacturing of 18 specific models of semiautomatic weapons, along with the manufacturing of high-capacity ammunition magazines that could carry more than 10 rounds. The ban had a provision that allowed it to expire in September 2004. … According to a 2004 study from the University of Pennsylvania, the number of people killed in mass shootings did go down generally during the years that the ban was in effect. The exception was 1999, the year that the shooting at Columbine High School happened. The number of mass shootings per year has doubled since the ban expired, but the researchers say it's difficult to discern whether there was a cause-and-effect relationship. http://abcn.ws/V1xhEJ

SCOTUS AND GUNS: COURT YET TO 'CLARIFY THE ENTIRE FIELD.' Even after the 2008 Supreme Court gun ruling, striking down D.C.'s gun ban, ABC's Ariane DeVogue reports that legal ambiguities remain: Gun control advocates, dismayed at the ruling, took heart in Scalia's words that "nothing in this opinion should be taken to cast doubt on longstanding prohibitions on the possession of firearms by felons and the mentally ill, or laws forbidding the carrying of firearms in sensitive places such as schools and government buildings." … Scalia, in his opinion in District of Columbia v. Heller, acknowledged that the Supreme Court had not fully addressed regulations. "But since this case represents this Court's first in-depth examination of the Second Amendment, one should not expect it to clarify the entire field," he said. http://abcn.ws/V3WItJ

SANFORD VS. SANFORD? After South Carolina Gov. Nikki Haley appointed Rep. Tim Scott to replace Sen. Jim DeMint following his resignation, Roll Call's Abby Livingston reports on the options to replace him: "Former South Carolina Gov. Mark Sanford is mulling a congressional comeback, with sources saying he might join the special election contest for Rep. Tim Scott's soon-to-be-vacant House seat. Sanford is 'studying' a run … Emerging as a possible candidate is former South Carolina first lady Jenny Sanford-Mark Sanford's ex-wife-who lives in the 1st District. One Palmetto State GOP strategist said Haley would likely back Jenny Sanford, who was on the governor's short list of possible Senate appointees, if she decides to run. … The other noteworthy name is Republican state Sen.-elect Paul Thurmond, son of the late Sen. Strom Thurmond. Scott defeated Thurmond by a 2-1 ratio in a 2010 primary runoff in an open-seat race for the 1st District." http://bit.ly/YfZi2C

WHITE HOUSE OFFERS NO GUN-CONTROL DETAILS. ABC's Mary Bruce reports: The day after President Obama pledged to "use whatever power this office holds" to prevent future tragedies like the massacre at Sandy Hook Elementary School, the White House offered few details on exactly what actions he plans to take to halt gun violence. "It's a complex problem that will require a complex solution. No single piece of legislation, no single action will fully address the problem," White House Press Secretary Jay Carney said. "I don't have a specific agenda to announce to you today. I would simply point you to what the president said last night about moving forward in coming weeks. And I would look for him to do that." http://abcn.ws/RBBXqc

GAY MARINE PROPOSES TO BOYFRIEND AT THE WHITE HOUSE. ABC's Devin Dwyer reports: U.S. Marine Corps Capt. Matthew Phelps made history Saturday at the home of his commander in chief. The 35-year-old active-duty officer proposed to his boyfriend, Ben Schock, 26, in the Grand Foyer of the White House at the end of a holiday tour. It's believed to be the first time two gay men have gotten engaged inside the White House, and a first for an active-duty member of the U.S. military. A transgender man proposed to his partner in the East Room earlier this year. http://abcn.ws/RBCAAa

HILLARY CLINTON RECOVERING, REVIEWING BENGHAZI REPORT. ABC's Dana Hughes reports: Secretary of State Hillary Clinton is feeling a bit better following the concussion she suffered early last week, but will continue to rest this week, State Department officials said. A U.S. official tells ABC News that Clinton is feeling more "like herself" and would like to go back to work, but doctors have advised it may take several weeks and want the secretary to rest. That is standard for concussion treatment. The secretary was set for a full week of events and work commitments, including testifying before the House Foreign Affairs and Senate Foreign Relations committees on Thursday, following the release of the State Department's internal investigation on the consulate attack in Benghazi, Libya in September. … Secretary Clinton received the report on Monday and is reviewing it at home. http://abcn.ws/12xEJhB

DICK'S PULLS GUNS AFTER SANDY HOOK. The chain is no longer selling guns, CNN's Susan Candiotti reports: Dick's Sporting Goods, one of the largest sporting goods retailers in the world, says it has removed all guns from its store nearest to Newtown, Connecticut, and is suspending the sale of certain kinds of semi-automatic rifles from its chains nationwide. The move was made out of respect for the victims and families of last week's Sandy Hook Elementary School shooting "during this time of national mourning," the store said in a statement Tuesday morning. "We continue to extend our deepest sympathies to those affected by this terrible tragedy," the statement said. http://bit.ly/RBCWa5

IN THE NOTE'S INBOX:

-ABORTION GROUP PRAISES SCOTT. After South Carolina Gov. Nikki Haley appointed Rep. Tim Scott to replace the resigned Sen. Jim DeMint, the anti-abortion Susan B. Anthony List sent this statement: "Congressman Tim Scott's rise to the U.S. Senate is great news to both the country and the pro-life movement," said SBA List President Marjorie Dannenfelser. "At a point where our nation is hungry for leadership, Congressman Scott has demonstrated compassion and clarity on the abortion issue, never backing down when asked the tough questions. He has made it clear that defending the most vulnerable is an indispensible first principle in his own political philosophy. We applaud Governor Haley for this choice and look forward to Tim Scott's pro-life leadership in the U.S. Senate."

WHO'S TWEETING?

@ethanklapper: Today is the first day since Hawaii became a state that it has not been represented by Daniel Inouye.

@BeschlossDC: Wary of choosing Asian-American, Humphrey '68 refused LBJ's suggestion of Inouye for VP saying, "it takes me a little too far, too fast."

@mckaycoppins: Pressure mounts for Obama to appoint the first female secretary of defense, reports @zekejmiller http://www.buzzfeed.com/zekejmiller/pressure-mounts-to-appoint-the-first-female-secret …

@ArletteSaenz: Perry on running for prez: It was an extraordinary experience…And looking back on it…I would do it again. http://bit.ly/V1O2zK

@Jordanfabian: RT @fixaaron: Fact: Pat Leahy is the first Senate pres pro tem ever to appear in a Batman movie.