Last minute talks aimed at averting a budget disaster which is due to hit the US tomorrow stalled this morning.
If Congress does not reach an agreement, around $US600 billion of spending cuts and tax increases will take effect from midnight on December 31 (4:00pm Tuesday AEDT) - sending the US economy off the so-called 'fiscal cliff'
Economists predict that would stifle the US economic recovery and send the country back into recession, spelling bad news for the global economy as well.
What is the fiscal cliff? Read our explainer.
This morning talks on brokering a deal ground to a halt as Democrats and Republicans blamed each other for a lack of progress.
Senate Republican minority leader Mitch McConnell warned that negotiators were still a long way from success, despite through-the-night talks.
He said he had received no response to a "good faith offer" to Senate Democrats, and called on his old friend and sparring partner, vice president Joe Biden, to join the fray in the hope of breaking the stalemate.
Senate Democratic leader Harry Reid agreed talks were at a standstill, saying Democrats were unwilling to agree to proposals to cut social security payments.
"This morning, we have been trying to come up with some counteroffer to my friend's proposal," Senator Reid told the Senate. "We have been unable to do that."
Senate Chaplain Barry Black opened the rare Sunday session of the chamber with a plea to God for lawmakers to avoid damaging the economy through their squabbling.
"Look with favour on our nation and save us from self-inflicted wounds," he said in a prayer.
Earlier president Barack Obama urged politicians to strike a deal, even if they must reach a compromise that lacks the significant deficit-reduction measures both sides had sought.
"We're at the point where, in just a couple of days, the law says that every American's tax rates are going up," Mr Obama said.
"Every American's pay cheque will get a lot smaller. And that would be the wrong thing to do for our economy."
We're at the point where, in just a couple of days, the law says that every American's tax rates are going up. Every American's pay cheque will get a lot smaller.
Mr Obama met with congressional leaders at the White House on Friday and declared himself cautiously optimistic about the chances of an agreement.
But he says nothing has materialised since then.
"I was modestly optimistic yesterday, but we don't yet see an agreement. And now the pressure's on Congress to produce," he told NBC's Meet The Press.
Mr Obama, sensing a mandate from his re-election last month, wants to raise taxes on the rich.
Republicans want only to close tax loopholes to raise revenue and demand significant spending cuts in return, notably to federal benefit programs like Social Security.
But if nothing is done by the deadline, all taxpayers will see an increase.
Mr Obama has chided Republicans for resisting a deal despite what he views as significant compromises on his part to cut spending and reform expensive social programs for the poor and elderly.
"The offers that I've made to them have been so fair that a lot of Democrats get mad at me," he said.
Both parties in this deeply polarised Washington had been hoping that we would get some details of a deal and that it could be reached later today (Sunday) so that they could start to brief their members on it. But as we know, time is running out. It's uncertain if those Senate leaders are going to get a deal.
If a compromise is reached, the Senate is going to be the first to vote on it and that could happen tonight (Sunday local time) or even tomorrow, which is New Year’s Eve here in the US.
And that would leave the House to have its vote before midnight on New Year’s Eve.
Washington correspondent Kim Landers
While each side must for the sake of appearances be seen to be seeking a deal, one way out is to go over the cliff, then fix the problem in the first days of next year.
Under that scenario, Republicans who are philosophically opposed to raising taxes could vote to lower the newly raised rates on almost all Americans without formally hiking taxes.
Politicians, while ruing the inability to work out a multi-trillion-dollar grand bargain in time, have said a pared-down version dealing mainly with taxes is within reach.
Citing unnamed people briefed on the talks, The Washington Post said one version under consideration would protect nearly 30 million taxpayers from paying the higher, alternative minimum tax rate for the first time and maintain unemployment benefits for two million people.
The plan also would halt a steep cut in Medicare reimbursements for doctors and preserve popular tax breaks for both businesses and individuals, such as those for research and college tuition, the report said.
But the two sides are still at odds over where to set the limits of wealthy - at $US250,000 or $US400,000 of annual income - and over taxes on inherited estates.
Nor has there been agreement on spending cuts so sought after by Republicans, who say excessive government spending is the main driver of US debt.
Mr Obama has warned that if an agreement is not reached in time, he will ask the Senate to hold an up-or-down vote on a basic package that protects the middle class from a tax hike, extends unemployment insurance, and "lays the groundwork for future... deficit reduction".
In a weekly Republican address, senator Roy Blunt expressed some optimism, saying that "going over the fiscal cliff is avoidable".
But he criticised Democrats for focusing mainly on taxes while setting aside government spending, arguing that such inaction "shouldn't be an option".