A fifth consecutive day of cross-party negotiations at the White House between President Obama and congressional leaders failed to make a breakthrough.
The president plans to hold a news conference to discuss the troubled talks at 1100 (1500GMT) on Friday.
The US must raise its $14.3tn (£8.9tn) debt ceiling to borrow beyond 2 August.
Failure to reach a deal would rattle a world economy still trying to put the 2008 downturn behind it, analysts say.'Childish'
On Thursday, Standard & Poor's became the second of the major credit rating agencies to place US debt under review, citing an increasing risk of a payment default.
Another ratings agency, Moody's, warned a day earlier that it might cut Washington's triple-A debt rating.
President Obama said that if congressional leaders could not "find agreement on the path forward" in the next 24-36 hours, the negotiations would have to continue into the weekend, according to Democratic and Republican aides.
The political impasse boiled over on Thursday to the Senate floor, where Majority Leader Harry Reid, a Democrat, called House Republican Leader Eric Cantor "childish".
Mr Reid said Mr Cantor "has shown he shouldn't even be at the table" in the debt talks at the White House.
Mr Cantor reportedly told President Obama during Wednesday evening's negotiations that the tax rises sought by Democrats simply were not going to happen.
He is also said to have urged the president to accept a short-term deal instead of a budget that would carry through to the presidential election in November 2012.
That is said to have prompted Mr Obama to say: "Enough is enough... I'll see you all tomorrow," before leaving the room.
US Federal Reserve chairman chief Ben Bernanke warned a Senate panel on Wednesday that a default would cause a "major crisis", adding it would be a "self-inflicted wound".
President Obama needs the Republican-led House of Representatives and Democratic-held Senate to agree a deal to trim the US deficit, and allow Washington to borrow beyond the 2 August deadline.
He has said he is willing to countenance cuts to social safety-net programmes dear to Democrats, as long as there are tax rises for the rich.
Republicans have rejected the latter proposal, saying that would stifle investment and job growth.