US Democrats have rejected a proposal from House of Representatives Republicans to extend the debt limit and reopen the federal government.
The White House criticised what it called an attempt to appease a small group of conservatives, but praised a parallel bipartisan Senate plan.
The White House balked at the House's proposed amendments to President Barack Obama's signature healthcare law.
The US must raise its $16.7tn (£10.5tn) debt limit by Thursday or risk default.
It remains unclear whether Congress can agree a deal in time to avert the economic calamity in the US and across the world that economists say could result.
The US House of Representatives would vote on Tuesday night on its bill to reopen the government and avoid default, said Republicans.
Meanwhile, Fitch credit agency placed the US AAA rating under review for a downgrade.
The Senate plan, outlined on Monday evening, would fund the government through mid-January and raise the debt ceiling until February, creating room for negotiators to agree a longer-term budget.
The House plan largely mirrored the Senate timeline until Representative Devin Nunes said on Tuesday afternoon it had been amended to fund the government only until 15 December.
The California Republican said the revised House plan also dropped earlier attempts to delay a medical device tax used to pay for healthcare subsidies under the Affordable Care Act.
The House plan would also eliminate healthcare subsidies for the president, vice-president, members of the president's cabinet, and members of Congress and their staff.
The health law passed in 2010, was subsequently validated by the Supreme Court, and was a central issue in the 2012 presidential election, which Mr Obama won handily. Many key provisions have already taken effect, and more begin next year.
On Tuesday, Mr Obama rejected what an aide described as Republicans' attempts to extort "ransom" while the government remained shut and the threat of a debt default loomed.
"Unfortunately, the latest proposal from House Republicans does just that in a partisan attempt to appease a small group of Tea Party Republicans who forced the government shutdown in the first place," said White House spokeswoman Amy Brundage, referring to a faction of hardline conservatives who hold significant sway in the House.
Later, Republican House Speaker John Boehner said that both parties were trying to find a way forward and that Tuesday morning's House plan was focused on "fairness for the American people under Obamacare".
"There have been no decisions about exactly what we will do," he told reporters on Tuesday. "There are a lot of opinions about what direction to go."
But following a meeting with Mr Boehner and GOP moderates on Tuesday Republican representative Charlie Dent told the media his "best estimate is that there aren't the votes to pass it".
House and Senate Democrats immediately joined Mr Obama in denouncing the House Republican proposal.
Senate Majority Leader Harry Reid said the plan was "an extreme piece of legislation and it's nothing more than a blatant attack on bipartisanship". He said it would never pass the Democratic-controlled Senate.
Mr Obama is scheduled to meet House Democrats on Tuesday afternoon as the clock ticks to Thursday's debt ceiling deadline.
Even if a deal is reached in the Senate, it is unclear whether Congress could act in time to pass legislation that would avert the 17 October default deadline.
Hardline conservatives such as Texas Republican Ted Cruz could use Senate rules to stonewall a vote.
In the House of Representatives, the Senate deal could meet fierce resistance from the Tea Party-aligned Republicans.
One of those conservative hardliners, Kansas Representative Tim Huelskamp, was quoted by the New York Times as labelling his upper chamber colleagues "the Senate surrender caucus".
"Anybody who would vote for that [Senate deal] in the House as Republican would virtually guarantee a primary challenger," he said.
Republicans have taken the brunt of blame for the latest fiscal cliffhanger to cripple Capitol Hill, according to opinion polls.
A Washington Post/ABC News survey on Monday found 74% of voters were unhappy with congressional Republicans' handling of the standoff, compared with a 53% disapproval rating for President Obama.
Some in the party have voiced concern that the affair could damage its prospects in next year's midterm elections.
The US Treasury has been using what are known as "extraordinary measures" to pay its bills since the nation reached its current debt limit in May. Those methods will be exhausted by 17 October, it has said.
Meanwhile, the government remains partially shut down because Congress failed to agree on funding by a 1 October deadline.
The impasse has closed a swathe of federal services and left hundreds of thousands of employees out of work.