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As the fiscal cliff looms, what's your New Year's message to Washington? Go to CNN iReport to share your video.

(CNN) -- With only hours left Monday to avert what economists predict will be a one-two punch to the U.S. economy, Senate Democrats and Republicans were trying to negotiate a last-minute deal aimed at heading off a year-end combination of spending cuts and tax increases that could trigger a new recession.

The Senate was scheduled to reconvene at 11 a.m. ET, when Majority Leader Harry Reid said he hoped to have an announcement despite acknowledging Sunday that there was "still significant distance between the two sides."

The negotiations hit a stumbling block Sunday over a Republican demand that a deal to avoid the "fiscal cliff" include changes to Social Security benefits, even as the two sides appeared close to agreeing on who would be required to pay more taxes once the Bush-era tax cuts expire.

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Over the weekend, Democrats offered to raise the income threshold for tax increases to $450,000, up from the $250,000 annual household income mark set by President Barack Obama, a Democratic source told CNN on Monday. Obama had initially set the target at $250,000 for households, but at one point had offered to shift the mark to $400,000 as part of a larger deal.

Republicans have since dropped their demand that changes to how Social Security benefits are adjusted for inflation be included in a deal, but not before Democrats and Republicans accused one another of gamesmanship in the negotiations.

Reid chastised Republicans for putting up the Social Security issue, while Senate Minority Leader Mitch McConnell appealed to Vice President Joe Biden to help "jump-start" negotiations after complaining that he had received no response to an offer he put on the table.

"I want everyone to know I'm willing to get this done, but I need a dance partner," said McConnell, R-Kentucky.

Reid, D-Nevada, had said earlier that McConnell had shown "absolutely good faith" in the talks, but "it's just that we are apart on some pretty big issues."

If nothing gets done before Monday at midnight, when the Bush administration's 2001 and 2003 tax cuts expire, broad tax increases will kick in, as will $110 billion in automatic cuts to domestic and military spending.

The nonpartisan Congressional Budget Office has predicted the combined effect could dampen economic growth by 0.5%, possibly tipping the U.S. economy back into a recession and driving unemployment from its current 7.7% back over 9%.

McConnell and Biden, who served together in the Senate for more than two decades, had a "pretty fruitful" conversation Sunday, said Sen. Bob Corker, R-Tennessee.

Top-level sources on both sides of the negotiations said on condition of anonymity that talks are primarily now in the hands of McConnell and Biden, and they are keeping Reid and House Speaker John Boehner, R-Ohio, informed.

As he headed home Sunday night, Reid was asked about progress, and he said: "Talk to Biden and McConnell."

Obama, meanwhile, laid the blame over the stalemate at the feet of Republicans.

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"They say that the biggest priority is making sure that we deal with the deficit in a serious way. But the way they're behaving is that their only priority is making sure that tax breaks for the wealthiest Americans are protected," he said Sunday on NBC's "Meet The Press."

"That seems to be their only overriding, unifying theme."

During the interview, Obama said he was willing to consider changing the way inflation is calculated for Social Security benefits, meaning that future Social Security recipients would receive less money over time, even though it was "highly unpopular among Democrats" and opposed by the AARP, the powerful lobby for seniors.

"In pursuit of strengthening Social Security for the long term, I'm willing to make those decisions," Obama said.

"What I'm not willing to do is to have the entire burden of deficit reduction rest on the shoulders of seniors, making students pay higher student loan rates, ruining our capacity to invest in things like basic research that help our economy grow. Those are the things that I'm not willing to do."

But a Democratic source, who did not want to be identified because of the closed nature of the talks, said members understand Obama proposed making inflation adjustments to Social Security benefits as an element of a larger deal that also would change how the federal debt ceiling is adjusted -- an element no longer included in the plans.

Most Democrats oppose the inflation adjustment to Social Security, known as "chained CPI," but many were wiling to go along with it as part of a larger deal, the source said.

The question of tax increases continues to be an issue, as well.

Many Republicans have opposed any increase in tax rates. Boehner suffered a political setback by offering a compromise -- a $1 million threshold for the higher rates to kick in -- that his GOP House colleagues refused to support.

Sunday night, Boehner met with House GOP leaders and told them to sit tight and stick together as he awaits news on whether the Senate can strike a deal.

After the meeting, Rep. Tom Cole, R-Oklahoma, told reporters that Boehner said: "I've stayed out of those negotiations."

"Every time we get involved in them, we sort of get burned, so we're going to let the Senate work its will, see what they do and what they send us, and we'll act accordingly," he said.

Sen. Chuck Schumer, D-New York, told ABC's "This Week" that he thought the chances of a short-term, last-minute deal brokered by Senate leaders were better than 50-50, while Sen. Lindsey Graham, R-South Carolina, told CNN that Obama will probably win the fiscal cliff battle, but it will do little to help the nation's deficit problem.

"The president will get a political victory, a trophy for the president politically, but it will not change our debt situation or reduce our deficit in any meaningful way," Graham said. "It will be a political victory that is hollow in nature when it comes to preventing our country from becoming Greece."

Other Republicans argued Sunday that Obama's plan hasn't done enough to limit spending.

"The president is doing nothing about the addiction that his administration has to spending. He's the spender in chief," Sen. John Barrasso of Wyoming said on CNN's "State of the Union."

CNN's Matt Smith, Jessica Yellin, Dana Bash, Deirdre Walsh, Lisa Desjardins, Ted Barrett and Ashley Killough contributed to this report.