US Congressional leaders have one more day to stop steep tax rises and spending cuts, known as the “fiscal cliff”, after talks ended with no deal.
Senators will continue to seek a compromise deal on Monday to send to the House of Representatives.
Failure to reach agreement by 1 January could push the US back into recession.
President Barack Obama has blamed Republicans for the deadlock. He said their “overriding theme” was protecting tax breaks for the rich.
Republicans and Democrats have been fighting for months over how to deal with the combination of automatic spending cuts and the expiration of Bush-era tax reductions at the new year.
Without an agreement, higher taxes will rise for virtually every working American and across-the-board cuts in government spending will kick in from Tuesday.
Analysts say this could significantly reduce consumer spending, leading the US economy to fall off the “fiscal cliff”.
After the latest round of intense negotiations in the Senate on Sunday the main sticking points reportedly include such key issues as the income threshold for higher tax rates and inheritance taxes.
If no agreement is reached on Monday, senators are expected to be given the chance to vote on a fallback plan proposed by President Obama.
That would renew tax cuts on earnings under $ 250,000 (£154,000) and extend unemployment benefits, but does not address the spending cuts.
Both the House and Senate are due to convene on Monday in a last-minute attempt to bridge the gap between the two sides. The Republican Speaker of the House, John Boehner, has insisted that the Senate act first.
The current stand-off has its roots in a failed 2011 attempt to tackle the government debt limit and budget deficit.
Republicans and Democrats agreed then to postpone difficult decisions on spending until the end of 2012.
Commentators say that even if a deal is reached, it will do little to reduce the original problem of the deficit and the government debt limit, raising the prospect of further political infighting early in the new year.
Senate Democratic leader Harry Reid and his Republican counterpart Mitch McConnell were locked in negotiations over the weekend.
The two senators appeared to admit before the 15:00 deadline (20:00 GMT) that negotiations were at a standstill, with their two parties still divided over core issues.
However late on Sunday, Senate Republicans said they were dropping their proposal to slow the growth of Social Security payments. The plan – which would have led to lower benefits to pensioners and the disabled – had been fiercely resisted by Democrats.
Meanwhile Senator McConnell said he had asked Vice-President Joe Biden for help in breaking the deadlock late on Sunday.
“I’m concerned with the lack of urgency here. There’s far too much at stake,” he said. “There is no single issue that remains an impossible sticking point – the sticking point appears to be a willingness, an interest or courage to close the deal.”
In his interview with NBC’s Meet the Press, broadcast on Sunday, Mr Obama said the priority was to ensure taxes do not rise for middle-class families, saying that would “hurt our economy badly”.
“That’s something we all agree on. If we can get that done, that takes a big bite out of the ‘fiscal cliff’,” he said.
There is also debate over where to set the threshold for tax rises. Democrats say the Bush-era tax cuts should be extended for all Americans except the richest – those with annual earnings of more than $ 250,000 (£155,000).
Republicans – some of whom have pledged never to vote for increased taxes – say the deficit is a consequence of excessive government spending.
They want the tax threshold set higher, at around $ 400,000, and for revenue to be raised by economic growth and cuts in social security and other services states are legally bound to provide.