The White House criticized 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 $16.7 trillion 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 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 December 15.
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 Barack Obama won handily. Many key provisions have already taken effect, and more begin next year.
On Tuesday, Barack 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 John 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 Barack 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.
President Barack 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 October 17 default deadline.
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