President Barack Obama has said he is “modestly optimistic” that Senate leaders can craft a bill that could win approval in both chambers of Congress.
If they fail, taxes will significantly rise for most Americans, raising fears of a US economic slowdown.
Republicans and Democrats tried to resolve the looming crisis in 2011 but failed, instead signing temporary agreements which postponed the deadlock until the end of 2012.
Democrat Senate leader Harry Reid and his Republican counterpart Mitch McConnell have been locked in negotiations over the weekend, in an otherwise closed-down Capitol.
According to the Washington Post, they have set themselves a deadline of 15:00 local time (20:00 GMT) to reach a compromise agreement, after which they will convene caucus meetings of their members and decide whether the measure has enough support to be put to a vote.
The Senate could then vote on the measure and allow the House of Representatives enough time on Monday to consider it, said the paper.
But Republican and Democratic leaders remain divided over core ideological issues about tax and government funding.
There is also debate over where to set the threshold for tax rises. Democrats say tax cuts introduced by former President George W Bush and now due to expire should be extended for all Americans except the richest, those with annual earnings of more than $250,000 (£155,000), who should pay more.
Republicans 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 mandatory spending programmes.
President Obama is scheduled to make a rare appearance on NBC’s Meet the Press on Sunday.
He has urged negotiators to reach a deal, even if the resulting legislation is an unhappy compromise for both sides which defers resolution of some elements under discussion.
The country “just can’t afford a politically self-inflicted wound to our economy,” he said, warning that if they fail, “every American’s paycheck will get a lot smaller”.
“Congress can prevent it from happening, if they act now,” he said.
Some Republicans have pledged never to vote for increased taxes. There are some indications they could oppose any deal which included higher taxes.
If Mr Reid and Mr McConnell cannot reach a deal by the end of the year, Mr Obama has said he will seek a vote to prevent tax rises on incomes up to $250,000 and ensure unemployment insurance is continued.
That, he says, is the “bare minimum” Congress should get done before 1 January.
End to benefits
The term fiscal cliff refers to the combination of almost $600bn (£370bn) of tax rises and spending cuts due to come into force on 1 January if Congress fails to pass new legislation.
- On 1 January 2013, tax increases and huge spending cuts are due to come into force – the so-called fiscal cliff
- Deadline was put in place in 2011 to force president and Congress to agree ways to save money over the next 10 years
- Fear is that raising taxes while massively cutting spending will have a huge impact on households and businesses
- Experts believe it could push the US into recession, and have a global impact on growth
Sweeping Bush-era tax cuts will expire, eventually affecting people of all income levels, and many businesses.
While some of the impact would be felt almost immediately, other effects would take longer to filter through. This could damage America’s recent fragile economic recovery and alarm global markets.
In addition, the US Treasury will hit its legal borrowing limit on 31 December of $16.4tn.
Last week, Treasury Secretary Timothy Geithner won a reprieve of about two months of time, but the debate on the borrowing ceiling will also need to be properly addressed in the new year.
The tax cuts and benefits set to expire include:
• A 2010 payroll tax cut, the expiration of which would prompt immediate wage-packet cuts
• Benefits for the long-term unemployed, which could mean more than two million Americans immediately stopped receiving payments
• Compensation for doctors treating patients on federal healthcare programmes
• Inheritance taxes are also likely to be affected if no deal is reached.
In addition, spending cuts mandated by a law passed to break a previous fiscal impasse in Congress will come into force, affecting both military and domestic budgets.
The cuts are expected to affect federal government departments and the defence sector, as well as hitting unemployment insurance and veterans’ support.