Senate Minority Leader Mitch McConnell (R-Ky.) and Vice President Joe Biden engaged in furious overnight negotiations to aver...

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Senate Minority Leader Mitch McConnell (R-Ky.) and Vice President Joe Biden engaged in furious overnight negotiations to avert the fiscal cliff and made major progress toward a year-end tax deal, giving sudden hope to high-stakes talks that had been on the brink of collapse, according to sources familiar with the discussion.

McConnell and Biden, who served in the Senate together for 23 years, only started talking Sunday, after negotiations between Senate Majority Leader Harry Reid (D-Nev.) and McConnell sputtered.

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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.

"The Leader and the VP continued their discussion late into the evening and will continue to work toward a solution. More info as it becomes available," a McConnell spokesman said.

It comes as Washington awakens on a chilly New Year's eve to a daunting reality: If lawmakers and the White House are not able to broker a last-minute deal on the fiscal cliff, the country will actually go over it.

(PHOTOS: 11 side effects of going over the cliff)

Going over the cliff is not how Americans want to start 2013: with hefty new tax hikes and spending cuts that could send the stock market plummeting, slash defense spending and interrupt an economic recovery that was just beginning to spark.

But after a weekend in which senators haggled over one obstacle to agreement after another, going over the cliff looked like real possibility, if not a probability. The McConnell-Biden talks look like they could avert this potential disaster.

If there's an agreement, it will come out of the Senate. Speaker John Boehner has said the House will take up whatever bill the Senate passes and either pass it, or amend it and send it back to the upper chamber.

The main hurdle remained over which income groups would be hit with tax hikes in the new year.

Democrats had proposed raising taxes on individuals who make more than $360,000 annually and families whose income is more than $450,000. And McConnell had countered with a tax hike for individuals above $450,000 and couples who earn more than $550,000 earlier in the evening Sunday.

But Democratic sources close to the talks said McConnell would have to go significantly lower to win support from their party, although that would make it more difficult for the GOP leader to win over fellow Republicans. Estate taxes, a chief concern for McConnell, remained a sticking point as well.

The back-and-forth shows the difficult political calculus both sides were making on the eve of a critical deadline. The drawn out negotiations were frustrating to many in both parties who are eager to see an agreement reached.

(PHOTOS: Fiscal cliff's key players)

"I've been here four years and I cannot believe negotiations have reached this level of gridlock. I am fed up with the stalling," said Alaska Democratic Sen. Mark Begich.

With no deal at hand, Senate leaders were preparing alternative plans to avoid the cliff's full impact, including a fall-back option floated by Democrats to force through an extension of current tax rates for families who make less than $250,000, as well as new spending measures to extend jobless benefits for two million unemployed Americans. Republicans were still weighing whether they'd demand 60 votes for passage of even a limited measure, though the prospects for such a bill in the GOP-controlled House remained bleak.

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Such a deal wouldn't fend off the sequester, billions of dollars in cuts to defense and domestic programs slated to begin on Jan. 2 and roll out over the next nine months.

The House Republican leadership moved Sunday night to give itself expedited authority to bring legislation to the floor in case the Senate actually passes a compromise bill Monday.

House Republicans, who turned against their own leadership last week, rallied around Speaker John Boehner (R-Ohio) on Sunday night, giving him a round of applause for his work in negotiating over the fiscal cliff.

But the more both sides negotiated this weekend, the more they seemed to remain in place.

After loud Democratic protests on Sunday, Republicans agreed to take off the table a controversial provision that would have cut Social Security benefits. But more hurdles soon emerged, including over automatic spending cuts set to take place next year, and the rates for estate taxes that are set to balloon if no deal is reached by the new year.

Key to the stalemate is the growing tension between McConnell and Senate Majority Leader Harry Reid (D-Nev.), the pair who took over the fiscal cliff talks Friday following weeks of fruitless discussion between President Barack Obama and Boehner.

Democrats are angry at McConnell, believing he's adopted for the Senate the "majority of majority" standard Boehner has demanded in the House. McConnell does not believe Reid is playing straight with him, saying the Nevada Democrats has shown little urgency by dragging his feet through the weekend of talks.

McConnell even called in Biden to help break the logjam, although the vice president has offered nothing different from Reid's position.

"There is still significant distance between the two sides, but negotiations continue," Reid said Sunday evening, announcing that the chamber would return Monday morning.

On Sunday afternoon, a new sticking point emerged over "turning off" the sequester, the tens of billions of dollars in spending cuts slated to hit the Pentagon and federal agencies beginning Jan. 2. Democrats want to use some of the revenue from the increased taxes of a cliff deal to postpone those cuts. Republicans, however, are objecting to that proposal, saying they want savings from other areas.

Democrats have floated a potential compromise to use a portion of the new revenue and other savings from a cliff deal -- a "50/50 split" -- to "turn off" the sequester, but it is unclear if GOP leaders will agree to that offer.

And Biden's inclusion in the negotiations -- similar to the role he played in previous legislative fights involving McConnell, an old Senate colleague -- sets up a "good cop, bad cop" scenario for Democrats, with Reid playing the heavy and Biden able to work more closely with GOP leaders on Capitol Hill.

But Democrats are not convinced McConnell or Boehner will be able to cobble together enough votes on their side of the aisle to support any bipartisan agreement.

Republicans, for their part, aren't sure Reid and Obama even want a deal, believing Democrats figure that they win politically if no agreement is reached and the country goes off the cliff.

Republicans were still weighing their strategy if Reid moves forward with a fall-back plan. If they consent to a simple majority vote, the bill could pass the Senate, putting House leaders in a difficult position on the eve of a cliff fall. But if Senate GOPers demand 60 votes, they could be blamed for blocking a last-ditch deal to avert massive tax hikes.

"We'd like to be able to offer some amendments" to a cliff deal, said Sen. John Cornyn of Texas, the incoming GOP whip. "It depends on the majority leader."

Leaving a Sunday afternoon caucus meeting, Florida Sen. Marco Rubio said that many GOP senators were ready to allow a simple majority threshold on a cliff deal, though he noted any individual senator could demand 60 votes for passage.

"By and large, members here, from what I've heard are willing to allow these things to be voted on in a simple majority fashion," Rubio said.

House Republicans -- who brought their chamber back to session Sunday -- are waiting for the Senate to pass a bill, and don't plan to move any bill on their own.

Some Republicans -- such as Nevada Sen. Dean Heller -- said they'd be willing to sign onto a deal with a tax-hike threshold of $400,000.

But Democrats are not sure that McConnell will ultimately agree to raising taxes on any income group, even those making $400,000 or more.

"McConnell knows exactly what it is going to take" to get an agreement with Reid and the White House, said one Democratic insider. "The question is can he bring himself to do it."

"We are still left with the proposal they've given that protects the wealthy and not the middle class and I am not going to accept that," Reid told reporters late on Sunday afternoon.

Administration officials predict the president will get what he wants on tax rates -- it's just a matter of how long Republicans want to stand in the way.

If Senate leaders are unable to reach a bipartisan compromise, the White House is confident that the Senate will pass the president's plan to extend the tax cuts on income below $250,000 either because McConnell will allow approval of the plan by a simple majority or because enough Republicans will help break a filibuster. They view several potential Republican defections, including Sens. Olympia Snowe of Maine and Sen. Dick Lugar of Indiana as upping the pressure on McConnell to strike a more-favorable deal for his party. Lugar said Sunday he didn't know how he'd vote on the Democratic plan.

It remains unclear what the president views as his tipping point. White House officials say Obama's willingness to accept a higher income threshold depends on what else is in a deal, but he would expect greater concessions from Republicans.

Earlier in the day, negotiations between Reid and McConnell suffered a "major setback" after Republicans demanded the inclusion of a new method for calculating entitlement benefits as part of the cliff package, according to Democrats.

The provision, known as "chained CPI," is opposed by many liberals because it would result in lower payments for Social Security beneficiaries.

While Obama backed the chained CPI provision as part of a major deficit package just two weeks ago, Democrats objected to including this as part of a scaled-down cliff deal.

Democrats insist they've already compromised on other issues, including raising the threshold for new taxes to around $400,000 annually, as well as showing flexibility on estate taxes, sources said.

But some Republicans were calling for inclusion of the chained CPI provision -- which would result in roughly $220 billion in savings over the next decade --in exchange for raising taxes.

GOP senators confirmed that McConnell dropped the chained CPI measure from his list of demands, but now say they want to make sure Obama and Democrats don't use new revenue from higher taxes to boost government spending.

"We are negotiating in good faith so we have taken that off the table," Sen. Kelly Ayotte (R-N.H.) said of the chained CPI.

Ayotte acknowledged that there was opposition to the chained CPI in her own caucus, saying more than half of Senate Republicans supported excluding it from any deal.

Ayotte said a Republican sticking point now is that new taxes not be used for new spending. "Where we are now is raising taxes for new spending and that's an issue," Ayotte said.

On the Senate floor early on Sunday, Reid ruled out any cuts to Social Security as part of any cliff agreement.

Democrats later left a closed-door Democratic Caucus meeting on Sunday afternoon united, with many prepared to go over the cliff if no amenable deal is reached.

"The world won't end -- remember Y2K?" said Sen. Tom Harkin (D-Iowa). "If this thing goes on, all of a sudden, the people find out there's a lot of revenue coming into the government -- and we have a sequester that we can deal with in January and February, and I think we will. I think then perhaps -- then Republicans won't have to vote to raise taxes, we'll all be voting to cut taxes."

Republicans suspected Democrats were not acting in good faith -- given the feeling among many that falling off the cliff is a viable option.

"The majority leader's staff informed us they would be getting back to us this morning at 10 a.m., despite the obvious time crunch we all have," McConnell said early Sunday. "It's now 2 p.m., and we have yet to receive a response to our good-faith offer. Now, I'm concerned about the lack of urgency here. I think we all know we're running out of time."

"There is no single issue that remains an impossible sticking point," McConnell added. "I'm willing to get this done, but I need a dance partner."

Absent a deal, Democrats were preparing for a long week in Washington.

"My expectation is we will be here probably every day for the next week," said Sen. Chris Coons (D-Del.).

Seung Min Kim, Ginger Gibson, Kate Nocera and Carrie Budoff Brown contributed to this report.