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

NOTABLES:

• FISCAL-CLIFF LATEST - ENTER JOE BIDEN: After talks stalled with Senate Majority Leader Harry Reid, Senate Minority Leader Mitch McConnell turned to Vice President Joe Biden, and all eyes are now on their negotiations. ABC's Matthew Larotonda, Jonathan Karl, and Sunlen Miller report that Vice President Biden has now re-emerged as a key player playing "a direct role" in trying to make a deal with Senate Republicans. Biden has been tapped because of his long-standing relationship with McConnell. A Democratic source says that McConnell seems to be genuinely interested in getting an agreement. The news dovetails with reports that the GOP has backed off a key Social Security measure that had stalled negotiations. According to sources, the row was sparked when the GOP offered a proposal that included a new method of calculating entitlement benefits with inflation. Called the "chained consumer price index," or Chained CPI, the strategy has been criticized by some Democrats because it would lower cost of living increases for Social Security recipients. http://abcn.ws/WenL2q

• OBAMA 'MODESTLY OPTIMISTIC': With time running out for Congress to reach an agreement, a senior White House official tells ABC News that President Obama is still "modestly optimistic" that a deal can be struck to prevent middle class taxes from increasing on New Year's Day. http://abcn.ws/WenL2q

• CLINTON HOSPITALIZED WITH BLOOD CLOT: ABC's Dana Hughes and Dean Schabner report: Secretary Hillary Clinton was hospitalized yesterday after a doctors doing a follow-up exam discovered a blood clot had formed, stemming from the concussion she sustained several weeks ago. She is being treated with anti-coagulants and is at New York-Presbyterian Hospital so that they can monitor the medication over the next 48 hours, Deputy Assistant Secretary Philippe Reines said. Her doctors will continue to assess her condition, including other issues associated with her concussion. They will determine if any further action is required, Reines said. Clinton, 65, originally fell ill from a stomach virus following a whirlwind trip to Europe at the beginning of the month, which caused such severe dehydration that she fainted and fell at home, suffering a concussion. No ambulance was called and she was not hospitalized, according to a state department official. http://abcn.ws/TBFAd5

• TODAY IN WASHINGTON: After yesterday's rare Sunday session the Senate is back today in session at 11 a.m., ABC's Sunlen Miller notes. Minority Leader Mitch McConnell, R-Ky., and Vice President Joe Biden will continue to work toward a solution, an aide says. Meanwhile, on the House side, ABC's John Parkinson hears from sources that the GOP Conference will meet at some point today (a time has not been set). And while the House waits on the Senate to act on the fiscal cliff, lawmakers will consider a lengthy list of non-fiscal cliff legislation. At the White House, President Obama has no public events on his schedule.

THE NOTE:

On Capitol Hill today, finding common ground means staying on solid ground and with just hours to go before the clock strikes midnight, there are finally last-minute signs of progress in the negotiations to avoid the fiscal cliff.

Vice President Biden and McConnell had "several conversations deep into the night," ABC News Chief White House Correspondent Jonathan Karl reported on "Good Morning America" and a spokesperson for McConnell described the talks as "good."

That's not exactly an assessment brimming with confidence, but as Karl notes, "good" is a giant leap forward from where talks had been headed over the last few days. And it comes just hours after both sides encountered what a Hill aide described as a "major setback."

Senate Majority Leader Harry Reid, D-Nev., pointed out yesterday that there was still "significant distance between the two sides" on several key sticking points.

And his Republican counterpart, Senate Minority Leader Mitch McConnell, R-Ky. said on the Senate floor: "I want everybody to know, I'm willing to get this done, but I need a dance partner."

McConnell has evidently found one in the vice president, and according to Politico's John Bresnahan, Manu Raju and Jake Sherman, "sources close to the talks said a deal is now more likely to come together but cautioned that obstacles remain, including how Speaker John Boehner and House Republican leaders react to any tentative agreement." http://politi.co/Z3UspE

Our Jon Karl notes that differences between Republicans and Democrats have narrowed on the threshold for increasing taxes on the wealthy and on the estate tax. The primary sticking point now appears to be on spending cuts.

Check ABC News throughout the day for the latest in the fiscal cliff negotiations from our reporters at the White House and on Capitol Hill. http://abcnews.go.com/politics

NOTED!

ABC's RICK KLEIN: No more kicking the can down the road - right? Except that's exactly what Congress is doing, even if it winds up doing something. The kind of mini-deal that's still in play at this late, late pre-cliff hour would actually worsen the deficit outlook - canceling a big chunk of planned tax hikes, delaying the promised tough spending cuts, and expanding spending on some items including unemployment insurance. That means it's possible that the next round of fiscal discussions will be more difficult to resolve, if resolution is even what can be reasonably expected when we get there. In many grim chapters about Washington dysfunction, this episode will be hard to beat.

"THIS WEEK" REWIND:

-SCHUMER'S ODDS: BETTER THAN 50-50. Sen. Charles Schumer, D-N.Y., is at least partly optimistic about a fiscal-cliff deal getting struck before the deadline, he told ABC's Jonathan Karl. There is "a real possibility of a deal," Schumer said, giving Congress and the White House "a little better than" 50-50 odds of reaching compromise. "On these big, big agreements, they almost all happen at the last minute," Schumer said. "So while an agreement is hardly a certainty, I certainly wouldn't rule it out." http://abcn.ws/Uz1O0r

-KYL: 'DIRE' CONSEQUENCES IF NO DEAL IS STRUCK. Arizona Republican sen. Jon Kyl agreed that there's a chance a deal could be struck and warned of the consequences if one isn't. "If we are not able to reach an agreement, it will be dire," Kyl said. "And that's from everybody from the Congressional Budget Office … to the Fed chairman, probably at least another million jobs lost, an unemployment rate over 9 percent, and putting us back into recession." http://abcn.ws/Uz1O0r

-ASK JON KARL - "THIS WEEK" WEB EXTRA. ABC's Jonathan Karl, who filled in for George Stephanopoulos as host of "This Week" on Sunday, answered questions from Facebook and Twitter about his new role at chief White House correspondent. One question from Phill Goldberg on Facebook: "How do you discern fact from fiction in the very tightly-controlled White House and DC media environment?" Answer from Jon Karl: "You always need to be fearful that you're being manipulated, you have to be skeptical of what is being said to you by any official source. That doesn't mean they're outright lying to you. Outright lies in this business tend to be pretty few and far between because a source who lies to you is not going to be a source you will look to again. … The best way to deal with that is to have multiple sources and talk to people on all sides of any given issue." WATCH the rest of the questions and answers: http://abcn.ws/ZMoT4T

THE BUZZ:

with ABC's Chris Good ( @c_good)

ANALYSIS: DEAL OR NO DEAL, CLIFF DEBACLE WILL LINGER. ABC's Rick Klein writes: The fiscal cliff is just the beginning. Regardless of whether Democrats and Republicans reach some kind of last-minute bargain to avoid the worst effects of tax hikes and spending cuts, the disaster that has been the fiscal cliff negotiations has broad implications for the Washington agenda in 2013 and beyond. The tone has been set for the new year, and possibly for the rest of President Obama's time in office: Washington's divisions are the only point that matters anymore. Call if dysfunction or call it just plain broken, just don't call it capable of even small legislative moves that involve compromise. … The other items Obama ticked through this weekend as part of his second-term agenda-immigration reform, energy and environmental policy, infrastructure investments, gun control-look like dreams in this environment. http://abcn.ws/12SYkd5

OBAMA: A SMALL DEAL IS THE BEST HOPE. President Obama sat for an interview with NBC's "Meet the Press," and ABC's Matthew Larotonda reports: With less than two days remaining for Congress to reach a budget agreement that would avoid the so-called "fiscal cliff," President Obama is suggesting that a small deal remains the best hope to avoid the perilous package of spending cuts and tax increases. The president said if Republicans agreed to raising taxes on top income earners it should be enough to avoid the triggers - mandated by law - that would execute the $607 billion measure economists agree would likely put the country back in recession. "If we have raised some revenue by the wealthy paying a little bit more, that would be sufficient to turn off what's called the sequester, these automatic spending cuts, and that also would have a better outcome for our economy long-term," he said. Saying the "pressure is on Congress to produce," the president did not specify what income level his party would deem acceptable as the cutoff for those who would see their tax rates remain at current levels. The president has called for expiration of the "Bush-era" tax cuts to effect household earnings over $250,000 since the campaign, but has reportedly floated a $400,000 figure in past negotiations. Speaker John Boehner once offered a $1 million cut-off in his failed "Plan B" proposal, which failed to garner enough support among the House Republicans. "It's been very hard for Speaker Boehner and Republican Leader McConnell to accept the fact that taxes on the wealthiest Americans should go up a little bit as part of an overall deficit reduction package," the president said. http://abcn.ws/TBHYke

OBAMA: NEWTOWN WAS THE 'WORST DAY' OF HIS PRESIDENCY. ABC's Matthew Larotonda reports on the president's "Meet the Press" comments about the Newtown, Conn., school shooting: "The question then becomes whether we are actually shook up enough by what happened here that it does not just become another one of these routine episodes where it gets a lot of attention for a couple of weeks and then it drifts away," he said. "It certainly won't feel like that to me. This is something that - you know, that was the worst day of my presidency. And it's not something that I want to see repeated." http://abcn.ws/YFIr4O

OBAMA: IMMIGRATION WILL BE PRIORITY. More on the president's NBC interview, from The Washington Times' Stephen Dinan: "President Obama says immigration is his major second-term priority, on par with his push for health care in his first term, according to an interview aired Sunday that continues to boost the issue to the top of the political conversation. 'Fixing our broken immigration system is a top priority. I will introduce legislation in the first year to get that done,' Mr. Obama told NBC's "Meet the Press" host David Gregory, who had asked the president what the second-term equivalent would be to his all-encompassing push for health care during his first term. He also said he would like to expand energy production and set the economy on firmer footing." http://bit.ly/UfzMWK

FISCAL CLIFF: WHAT'S ON THE LINE? If the cliff talks fail, the average American family would see a tax hike of $3,446 according to the Tax Policy Center at the Brookings Institution, ABC's David Muir reported for "World News." Middle incomes would be hardest hit, with tax rates nearly doubling for married couples earning $60,350 - $72,300, from 15 percent to 28 percent. http://abcn.ws/ZOWZVT

OMINOUS SENATE PRAYER: 'SAVE US FROM SELF-INFLICTED WOUNDS.' ABC's Sunlen Miller reports: The Senate on Saturday opened its first session in the days between Christmas and New Years since 1962 with an ominous prayer, as Congress and President Obama scramble to come up with a deal to avoid the fiscal cliff. "Let us feel your presence today on Capitol Hill," Senate Chaplain Barry Black prayed, opening up the day in the Senate. "As we gather with so much work undone, guide our lawmakers with your wisdom. Lord, show them the right thing to do and give them the courage to do it." With just a matter of hours before the nation goes over the so-called fiscal cliff without a deal, Black prayed for "shelter" in the "midst of the storm, regardless of how high the waters rise," for the legislators. http://abcn.ws/VSTk0P

A 'MAJOR SETBACK' ON SUNDAY. ABC's Jonathan Karl reported Sunday afternoon: Democratic Senate Leader Harry Reid on Sunday rejected the latest offer from Republican Leader Mitch McConnell, stalling tense last minute negotiations and pushing the country that much closer to the fiscal cliff as the senators seemed unable to find a bipartisan deal before automatic tax cuts and spending hikes kick in for the new year. A senior Democratic aide tells me that, although talks continue, the McConnell offer was "a major setback.' 'We are hugely disappointed,' the aide aid tells ABC News. http://abcn.ws/TBGLJr

GRAHAM: NO DEBT LIMIT INCREASE WITHOUT ENTITLEMENT REFORM. ABC's Michael Ono reports: Senator Lindsey Graham, R-S.C., said on Sunday that he would vote no to raise the debt ceiling, if concessions to reform Social Security and Medicare were not made, despite a previous statement by Graham to suggest that most Republicans were never willing to stomach a U.S. default back in 2011. "Why would I raise the debt ceiling again unless we address what put us in debt to begin with? I'm not going to raise the debt ceiling unless we get serious about keeping the country from becoming Greece, saving Social Security and Medicare," Graham said today on "Fox News Sunday." Graham's not alone. House Speaker John Boehner, R-Ohio, said in an interview earlier this month on "Fox News Sunday" that House Republicans will never give up control of the debt ceiling. "It's the only way to leverage the political process to produce more change than what it would if left alone," Boehner said. http://abcn.ws/VSW8Lv

IN THE NOTE'S INBOX:

-OP-ED: WHATEVER HAPPENED TO CUT, CAP AND BALANCE? Colin Hanna, president of the conservative group, Let Freedom Ring, writes in USA Today about how, he says, we might have avoided the fiscal cliff debate altogether: "We could have avoided the current predicament. In June of 2011, a rare coalition of outside groups and Congress proposed a solution that would indeed have solved our debt crisis - it was called Cut, Cap and Balance. The plan was simple - cut current spending now, cap future spending as a percentage of our overall economy and pass a Balanced Budget Amendment through Congress and send it to the States for ratification. Unlike the super committee or the present brinkmanship between the President and Speaker Boehner, Cut Cap and Balance was a solution, not just a deal. It addressed our spending problem in the short term, medium term and long term. Had that passed, we would have cut over $100 billion in the first year, over one trillion in 10 years, capped future spending to between 18 and 20% of gross domestic product annually, and the states would now be debating the Balanced Budget Amendment individually." http://usat.ly/S04q9n

WHO'S TWEETING?

@ktumulty: Breaking news: Fiscal cliff talks remain on the precipice of progress.

@mattgutmanABC: Sen Manchin to @nytimes : "something has gone terribly wrong when biggest threat to our American economy is the American Congress."

@BuzzFeedAndrew: Jon Huntsman calls the Republican Party "devoid of a soul." http://www.telegraph.co.uk/news/worldnews/republicans/9771589/Republican-party-is-devoid-of-a-soul-says-Jon-Huntsman.html …

@joshledermanAP: Check out new column from @AP political editor Liz Sidoti - Gun debate revives enduring American fight http://bit.ly/Uz3bw3

@JesseFFerguson: Congrats to @amygdudley and @adamslily and new Senate comms team for @timkaine. Great pick. Great team w/ @henry_mike.