US political rivals are cautiously optimistic about the chances of raising the $14.3tn (£8.7tn) debt limit by Tuesday and averting possible default.
Republican Senate leader Mitch McConnell said the sides were “very close” to a $3tn deal after talks with Vice-President Joe Biden.
Senior Senate Democrat Richard Durbin spoke of “a more positive feeling”.
There are hopes a deal may be agreed before a procedural vote in the Democrat-dominated Senate shortly.
That in turn would allow for a new vote in the Republican-held House of Representatives before the Tuesday deadline.
America limits by law the total amount of debt its government can run up in order to pay its bills, and the Obama administration is under mounting financial pressure.
“We have to get this solved,” White House senior adviser David Plouffe told NBC television on Sunday. “Today is obviously a critical day.”
Battle of the bills
In a sign of the level of anxiety over the issue, troops in Afghanistan asked Adm Mike Mullen if they would be paid.
The admiral, who as chairman of the joint chiefs of staff is on a visit to southern Afghanistan, said he could not tell if the US failed to raise the debt limit.
I suspect the difficult thing will not be the leaders sealing a deal but selling it to Republicans in the House, and perhaps Democrats in the Senate. ”
Democrats and Republicans have so far rejected each others’ proposals, proposing and rejecting each other’s bills in the two houses of the divided US Congress.
President Barack Obama backs a bill proposed by Democratic Senate Majority Leader Harry Reid, which would cut $2.2tn from deficits and raise the debt ceiling by $2.7tn, meaning the issue would not have to be revisited until after the 2012 elections.
Late on Saturday, Mr Reid postponed the procedural vote on his bill to Sunday afternoon.
“There are negotiations going on at the White House to avert a catastrophic default on the nation’s debt,” he said, adding that there was “still a distance to go”.
The House of Representatives rejected the Reid bill 246-173 on Saturday afternoon, even though the Senate had not voted on it.
House Republicans had passed their own plan, drawn up by speaker John Boehner, to make some $900bn in spending cuts and raise the debt ceiling by a similar amount.
But the Boehner plan would require another vote next year, in the midst of the next presidential campaign, and proposes a so-called “balanced budget amendment” to the US constitution.
The White House and the Senate leadership are opposed to both of these proposals, and the Boehner plan was rejected, in turn, by the Senate.
Speaking on CNN on Sunday, Mr McConnell said negotiators were “very close” to striking a deal.
He earlier called on Democrats to end their “charade” so that negotiations could be pursued with the president.
“We are now fully engaged with the one person in America out of 307 million people who can sign this bill into law,” he said before his talks with Mr Biden.
Mr Obama himself has reiterated that any solution must be bipartisan.
“Congress must find common ground on a plan that can get support from both parties in the House and in the Senate, and it has to be a plan that I can sign by Tuesday,” he said.
Meanwhile, the US Treasury is already drawing up emergency plans in case a deal is not reached by Tuesday.
Experts say the government has enough cash to keep functioning for another week or so after that.
US parties hopeful of debt deal