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 wiling 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.