(CNN) -- Congress trooped back to work on Sunday to face a combination of spending cuts and tax increases set to kick in within hours and President Barack Obama pressuring congressional Republicans to cut a last-minute deal.
Both the House of Representatives and the Senate went back into session Sunday afternoon. But leaders hit what a Democratic source familiar with the talks called a "major setback" when Republicans insisted that changes to how Social Security benefits are adjusted for inflation be part of the deal.
Using what's known as "chained CPI" would change the way Social Security benefits are adjusted for inflation, effectively meaning that Social Security recipients would receive less money over time. The Democratic source said party members consider that a "poison pill."
In the Senate, Minority Leader Mitch McConnell, R-Kentucky, complained that he had received no response to a proposal he made Saturday night and has asked Vice President Joe Biden to help "jump-start" negotiations.
"I want everyone to know I'm willing to get this done, but I need a dance partner," McConnell said.
A source close to the process told CNN that McConnell and Biden had spoken twice by mid-afternoon Sunday. Meanwhile, Majority Leader Harry Reid conceded that "at this point, I don't have a counteroffer to make."
Reid, D-Nevada, said McConnell has shown "absolutely good faith" in the talks, but "it's just that we are apart on some pretty big issues."
Neither Reid nor McConnell disclosed any details of the GOP offer. But in an interview broadcast Sunday, Obama told NBC's "Meet the Press" that Republicans are responsible for the stalemate that brought lawmakers back to Capitol Hill on a weekend.
"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," Obama said. "That seems to be their only overriding, unifying theme."
Obama said the Senate should go ahead and vote on legislation to make sure middle-class taxes are not raised and that 2 million people don't lose unemployment benefits.
"If we can get that done, that takes a big bite out of the fiscal cliff," he said. "It avoids the worst outcomes."
If nothing gets done before Monday night at midnight, the expiration of the Bush administration's 2001 and 2003 tax cuts will increase tax rates, damaging the economy and costing the average middle-class family about $2,000, he said, repeating the term "middle-class" numerous times throughout the interview.
At stake in the negotiations, according to numerous economists, is the fate of a still fragile U.S. economy that could be pushed back into a recession by the broad tax hikes and automatic $110 billion in cuts to domestic and military spending -- the result of the 2011 standoff over raising the federal debt ceiling. The nonpartisan Congressional Budget Office predicts the combined effect could dampen economic growth by 0.5% and drive unemployment back to 9.1% by the end of 2013.
Obama told NBC that he was willing to consider using chained CPI to adjust Social Security, 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," he 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."
A Senate Republican leadership source pointed to the president's comments Sunday. But the Democratic source, who did not want to be identified because of the closed nature of the talks, said members understand Obama proposed using chained CPI in earlier talks with Rep. John Boehner, the Republican speaker of the House, as an element of a larger deal that also would change how the federal debt ceiling is adjusted, which is no longer included in the plans.
Most Democrats oppose chained CPI, but many were willing to go along with it as part of a larger deal, said the source.
On taxes, meanwhile, Democrats are arguing that taxes should go up for those making $250,000 or more, though some discussions have involved the possibility of raising that figure to a $400,000 threshold.
The Democratic source said party members are currently "going outside their comfort zone" in these talks with regard to tax rates -- keeping tax rates in place for higher income households than the president wants. The source also said Democrats are negotiating with Republicans on extending the current lower estate tax rate, a big issue for many Republicans as well as moderate Democrats.
Sen. Chuck Schumer, D-New York, told ABC's "This Week" he thought the chances of a short-term, last-minute deal brokered by Senate leaders were better than 50-50.
"I've been a legislator for 37 years, and I've watched how these things work on these big, big agreements," Schumer said. "They almost always happen at the last minute. Neither side likes to give up its position. They eyeball each other till the very end. But then each side, realizing that the alternative is worse, comes to an agreement."
And Sen. Olympia Snowe, R-Maine, told CNN's "State of the Union" that she expects Congress will vote to extend tax cuts for incomes below $250,000 -- perhaps below $400,000 -- before midnight Monday.
"I think it would be horrific for the country if at this time, the final days of this legislative session that already has reached historic proportions of failure, that we would now culminate in failure to extend these tax cuts," said Snowe, who is on her way out of office. A Senate agreement "would build momentum" for the move in the House, she said.
Many Republicans have opposed any increase in tax rates. Boehner, R-Ohio, 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.
After the Obama's NBC interview, Boehner said the president needs to stand up to his own party and insisted it was the president "who has never been able to get to 'yes.'"
"The House has passed legislation to avert the entire fiscal cliff, and the president has never called for the Senate to act on those bills in any way. He instead has simply allowed the Democratic-controlled Senate to sit on them and lead our economy to the edge of the fiscal cliff," Boehner said in a statement issued by his office. "I am pleased Senators from both parties are currently working to find a bipartisan solution that can finally pass that chamber. That is the type of leadership America needs, not what they saw from the president this morning."
Sen. Lindsey Graham, R-South Carolina, said the chances are "exceedingly good" that some type of deal will be reached by Monday night.
"I think, whatever we accomplish, political victory to the president, hats off to the president. He stood his ground. He's going to get tax rate increases, maybe not (on people making) $250,000, but upper-income Americans," Graham said on "Fox News Sunday."
"And the sad news for the country is that we have accomplished little in terms of not becoming Greece or getting out of debt."
Other Republicans argued Sunday that the resistance to Obama's plan is based on his refusal to adequately 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."
Republican Rep. Darrell Issa of California echoed those remarks. "Even if you put back all the revenue you would get from those higher taxes, you still have a deficit. That's what we're trying to change," he said.
Obama rejected such complaints, telling NBC that he has cut more than a trillion dollars in spending.
"I offered over $1 trillion in additional spending cuts so that we would have $2 of spending cuts for every $1 of increased revenue," he said on NBC.
The president also emphasized that he had campaigned on "a balanced approach" that would increase taxes on the wealthy and that the majority of Americans have made clear they support such a plan.
The idea of maintaining tax cuts for 98% of Americans, while allowing tax cuts to expire for the wealthiest, was once part of "a pretty mainstream Republican agenda," he argued, adding that opposition "is an indication of how far certain factions inside the Republican Party have gone."
The interview, recorded Saturday, marked the president's first appearance on a political talk show in three years.