Leaders in the US Senate are attempting to strike a last-minute deal to avoid huge tax hikes and spending cuts set for January 1.
Economists warn the $500bn in fiscal pain due to hit in the New Year could send the country back into recession, and destabilise the global economy in the process.
But despite feverish work behind closed doors by aides to both leaders in the Democrat-controlled Senate on Saturday a deal palatable to both sides is still elusive.
US Senate Majority Leader Harry Reid said has made a counteroffer to a Republican proposal put forward on Saturday but admitted "serious differences" remain.
The two sides have reportedly moved closer on tax increases while Republicans have indicated they could withdraw a contentious proposal to slow the growth of social security retirement benefits.
Senate Republican leader Mitch McConnell said he has asked Vice President Joe Biden to become involved in a last-minute effort to reach an agreement.
He added that there was no single issue blocking an agreement but that "the sticking point appears to be a willingness, an interest, or courage to close the deal".
"I'm willing to get this done, but I need a dance partner," Mr McConnell said.
Both the Senate and the House of Representatives would have little time to debate and then pass a deal that has eluded the White House and Congress for weeks.
Barack Obama, who called congressional leaders to the White House on Friday, addressed the crisis once more as he appeared on NBC's Sunday morning talk show Meet the Press.
Mitch McConnell and Harry Reid still heading in different directions
The President said Republicans were unwilling to see tax rates raised for the richest taxpayers.
"They say that their biggest priority is making sure that we deal with the deficit in a serious way," Mr Obama said.
"But the way they're behaving is that their only priority is making sure that tax breaks for the wealthiest Americans are protected.
"That seems to be their only overriding, unifying theme," he added.
If a comprmise can be found, the two parties will then decide whether to put it to the vote on New Year's Eve in the Senate and then the Republican-controlled House of Representatives.
President Obama has pressed lawmakers to clinch a deal, even if they must reach a compromise that lacks the significant deficit-reduction measures both sides had sought.
"I was modestly optimistic yesterday, but we don't yet see an agreement," the President told NBC in the interview recorded on Saturday. "And now the pressure's on Congress to produce."
At least one senior Republican said he was optimistic of a deal, and a "political victory" for Mr Obama.
Senator Lindsey Graham told Fox News that the odds are "exceedingly good" a deal can be done.
"I don't think people want to go over the cliff," he said.
The US is facing the fiscal cliff because tax rate cuts dating back to George W Bush's presidency expire at the end of the year.
Mr Obama originally insisted on letting the tax cuts expire on households earning more than $250k (£154k) but later upped that threshold to $400k (£246k).
The pending reductions in spending, which will hit everything from social programmes to the military, were put in place last year as an incentive to both parties to find ways to cut America's soaring deficit.