"There are still serious differences between the two sides," said Senate Democratic leader Harry Reid.
Progress still appeared possible after the two sides narrowed their differences on tax increases and Republicans indicated they would withdraw a contentious proposal to slow the growth of Social Security retirement benefits.
Failure to secure a deal would deliver a heavy blow to the U.S. economy just as it is showing signs of a quicker recovery. Planned tax increases and spending cuts would suck $600 billion out of the economy and again force up unemployment, which had shown signs of improving.
Senate Republican leader Mitch McConnell talked several times to Vice President Joe Biden by phone in the hope of breaking the standstill. "I'm willing to get this done, but I need a dance partner," McConnell said.
Any agreement needs to be rushed through both chambers of Congress before midnight on Monday. But, even if the two sides reach a deal, procedural barriers in the Senate and the House of Representatives make quick action difficult.
Buoyed by his re-election in November, President Barack Obama has insisted that any deal must include a tax increase on the wealthiest Americans, who have seen their earnings rise steadily over the past decade at a time when income has stalled for the less affluent.
Many conservative Republicans in the House of Representatives oppose a tax hike on anyone, no matter how wealthy.
The two sides were close to agreeing to raise taxes on households earning around $400,000 or $500,000 a year - higher than Obama's preferred threshold of $250,000 - several senators told reporters.
Republicans aim to pair any tax increase with government spending cuts to benefit programs that are projected to grow ever more expensive as the population ages in coming decades.
But their proposal to slow the growth of Social Security benefits by changing the way they are measured against inflation met fierce resistance from Democrats. Obama included the proposal, known as "chained CPI," in an earlier proposal, but many of his fellow Democrats remain opposed.
'POISON PILL'
"We consider it a poison pill - they know we can't accept it. It is a big step back from where we were on Friday," a Senate Democratic aide said.
Several Senate Republicans said they would support taking that idea out of the discussion. "Most of us agree the chained CPI is off the table in these negotiations," Senator John McCain said on Twitter.
In a rare appearance on NBC's "Meet the Press," Obama pressured lawmakers to reach a deal.
"If people start seeing that on January 1st this problem still hasn't been solved... then obviously that's going to have an adverse reaction in the markets," he said, adding that he had offered Republicans significant compromises that had been rejected repeatedly.
Obama said he would try to reverse the tax hikes for most Americans if Congress fails to act.
John Boehner, the House speaker, rejected Obama's accusations that Republicans were not being amenable to compromise.
"The president's comments today are ironic, as a recurring theme of our negotiations was his unwillingness to agree to anything that would require him to stand up to his own party," he said in a statement. (Additional reporting by Tabassum Zakaria, Jeff Mason, David Lawder, Fred Barbash and Richard Cowan. Writing by Andy Sullivan; editing by Alistair Bell and Jackie Frank)
