The White House has warned that President Obama could veto a debt limit plan proposed by top House Republicans.
Meanwhile, Speaker John Boehner's plan to trim public spending and raise the limit met with resistance from rank-and-file members of his own party.
A House of Representatives vote on the plan was delayed from Wednesday after doubts arose over the cuts it proposed.
Washington remains deadlocked as a deadline to increase the government's borrowing authority looms on 2 August.
The US runs a budget deficit that topped $1.5tn (£920bn) this year, and has amassed a national debt of $14.3tn.
The government's authority to borrow more money has expired, and the US risks a first-ever default on its debt obligations if congressional and White House negotiators are unable to agree on a plan to increase the debt limit by 2 August.
The debt limit has been raised dozens of times in recent decades, mostly without partisan debate.
This year, though, conservative Republicans refused to allow an increase unaccompanied by dramatic cuts to the US budget deficit.
House of scorecards
The latest round of bargaining began on Monday when Mr Boehner and Senate Democrats offered competing plans to raise the debt limit and cut spending.
The plans differed in size and scope, and neither would raise new tax revenue - in recognition of Republicans' intransigence on that point.
Mr Boehner's plan would also require another debt limit agreement in about six months, something Mr Obama has publicly declared he will not accept.
On Tuesday, the White House budget office said in a statement that the Obama administration "strongly opposes" Mr Boehner's plan, adding that if it is presented to Mr Obama "the president's senior advisors would recommend that he veto this bill".
Mr Boehner was forced to rewrite his plan after the Congressional Budget Office, the official non-partisan score-keeper in fiscal legislation, said it would generate less than the $1.2tn (£730bn) in budget savings he had initially announced.
It was also slow to win support from rank-and-file Republicans in the House of Representatives, who have been pushing for steeper cuts.
Reports on Tuesday night said the legislation, scheduled for debate in the House on Wednesday, would now not make it to the floor until Thursday.
In prime-time back-to-back TV addresses on Monday evening, Mr Obama and Mr Boehner accused each other of intransigence on the debt issue.
Speaking on Tuesday, Mr Boehner said: "I think I made it pretty clear last night: the president's looking for a blank cheque."
"It's reasonable," Mr Boehner said of his plan. "It's responsible. It can pass the House, and it can pass the Senate."
He called on members of both parties to consider supporting what he called his "common sense plan... to put America's fiscal house back in order" when it arrived on the floor of the House on Wednesday.
The Republican majority leader in the House of Representatives, Eric Cantor, said of Mr Obama's speech on Monday night: "There was no evidence that he has a plan. He doesn't like our plan, but he has not put a plan forward yet.
"The president spent a lot of time talking about millionaires, billionaires, corporate jet owners, things that have nothing to do with the debate right now."
'Playing chicken'
In the Senate on Tuesday, Democratic Senate Majority Leader Harry Reid challenged Republicans to back his own plan - a no-taxes, government-cuts proposal to trim $2.7tn over a decade.
It would protect social programmes for the poor and elderly and a public pension programme - all popular among Democrats, while not raising new tax revenue.
The 10-year plan includes $1.2tn in cuts to defence and other discretionary spending and $1tn in savings from winding down the wars in Iraq and Afghanistan.
Later on Tuesday, White House Press Secretary Jay Carney accused the Republicans of trying "to play chicken with our economy". He said Mr Reid's plan was a much better option because it "represents compromise".
"The United States hit its debt limit in May, and since May the treasury secretary... has exercised all the wiggle room available to him and that runs out on 2 August," Mr Carney said.
He added: "It's whistling past the graveyard to suggest that it's some sort of game and the risks aren't enormous, because they are."
If the debt ceiling is not raised, the US Treasury could run out of money to pay all of its bills - which could lead to interest rate rises, threaten the US economy and in turn the global recovery.
