The Note's Must-Reads are a round-up of today's political headlines and stories from ABC News and the top U.S. newspapers. Posted Monday through Friday right here at www.abcnews.com

Compiled by ABC News' Jayce Henderson and Amanda VanAllen

SENATOR DAN INOUYE ABC News' Sunlen Miller: " Sen. Dan Inouye Dies, In Office Since '59" 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. Inouye's office confirmed the senator's passing to ABC News. LINK

FISCAL CLIFF The Hills' Erik Wasson and Russell Berman: " Obama makes new fiscal offer; Boehner says it's not enough" President Obama made a new fiscal cliff offer Monday that would raise ?$1.2 trillion in taxes and lift the debt limit for two years, and Speaker John Boehner (R-Ohio) rejected it. The president made the offer to the Speaker in a 45-minute meeting at the White House on Monday, in the latest sign of the quickening pace of negotiations to avoid the more than $500 billion in automatic tax increases and spending cuts due in January. LINK

The Los Angeles Times' Christi Parsons and Lisa Mascaro: " Obama makes a substantial counteroffer on fiscal deadline" President Obama trimmed his demand for tax increases on the wealthy Monday, making a substantial counteroffer as he and House Speaker John A. Boehner reconvened privately at the White House. Crucial differences remain, but the quickened pace of the budget talks suggested the men are engaged in a serious effort to bridge the partisan divide before the holidays - and before the year-end "fiscal cliff" leads to economically dire tax increases and spending cuts. LINK

Politico's Carrie Budoff Brown and John Bresnahan: " Obama makes new offer to narrow gap on cliff" President Barack Obama and House Speaker John Boehner made significant progress Monday toward a fiscal cliff deal, as Obama's new offer on tax rates moved the two sides closer to an agreement. But questions remained over whether Boehner could sell the key points to Republicans at a pivotal meeting Tuesday. The progress is fragile, and the next 24 hours are critical as lawmakers from both parties and interest groups on all sides weigh in. LINK The New York Times' Jonathan Weisman: " Obama's New Offer on Fiscal Crisis Could Lead to Deal" President Obama delivered to Speaker John A. Boehner a new offer on Monday to resolve the pending fiscal crisis, a deal that would raise revenues by $1.2 trillion over the next decade but keep in place the Bush-era tax rates for any household with earnings below $400,000. The offer is close to a plan proposed by the speaker on Friday, and both sides expressed confidence that they were closing in on a major deficit-reduction plan that could be passed well before January, when more than a half-trillion dollars in automatic tax increases and spending cuts would kick in. LINK

GUN CONTROL The New York Daily News' Kristen A. Lee: " Pair of gun rights loyalists call for action after Sandy Hook massacre" Two pro-Second Amendment Democratic senators signaled their support for tougher gun control on Monday in a dramatic sign of a shifting political landscape following the Sandy Hook Elementary School massacre. West Virginia Sen. Joe Manchin, who wielded a hunting rifle in a 2010 campaign ad, was the first to suggest a change of heart on Monday morning. LINK

The Washington Times' Stephen Dinan: " Gun-limit advocates find a rare juncture" The last time either chamber of Congress took on gun control was in 2004, when the Senate considered a pro-gun bill, ended up adding three major gun control measures - then killed it, saying the whole thing had become too messy. For more than a decade, gun rights supporters have held the upper hand in Congress, foiling more restrictions and steadily erasing bans such as carrying guns on Amtrak trains or into national parks. LINK

USA Today's Aamer Madhani: " White House offers no details on gun-control strategy" While pressure from the public and some gun-control advocates mounts in the aftermath of the Newtown, Conn., school shooting, the White House hasn't laid out any specifics on how President Obama plans to tackle the scourge of gun violence that he declared has become far too routine. The president spoke passionately about the need to take decisive action during his remarks at memorial services honoring the victims Sunday. LINK

Bloomberg's Phil Mattingly and Jonathan Salant: " Lawmakers Vow Tougher Gun Laws as Obama Weighs Next Steps" U.S. lawmakers yesterday responded to the killings in Connecticut with plans to hold hearings and introduce legislation, as the White House reiterated President Barack Obama's support for a new ban on assault weapons. The congressional response comes in the wake of the school shooting that claimed the lives of 20 children and 6 adults. Their proposals may be bolstered by policy options from the Justice Department as Obama pursues his vow to "use whatever power this office holds" to prevent another mass shooting. LINK

The Washington Post's Scott Wilson and Philip Rucker: " Obama asks Cabinet members for proposals to curb gun violence" President Obama on Monday began the first serious push of his administration to attempt to reduce gun violence, directing Cabinet members to formulate a set of proposals that could include reinstating a ban on assault rifles. The effort will be led by Vice President Biden, according to two people outside the government who have spoken to senior administration officials since Friday, when a gunman killed his mother and rampaged through Sandy Hook Elementary School in Newtown, Conn., killing 20 children, six adults and himself. LINK

ABC NEWS VIDEOS " President Obama Pledges Action to Prevent More Tragedies" LINK " Hillary Clinton Faints, Suffers Concussion" LINK

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