House Speaker John Boehner had been trying to convince rank and file lawmakers to vote for his bill on Thursday, but, after a delay of a few hours, the vote was cancelled.
There are now serious doubts about whether Boehner’s bill can be passed in time.
Any bill passed in the House must also be approved by the Senate and President Barack Obama, but Democrat leaders and the White House have said they cannot tolerate Mr Boehner’s bill.
Congress must raise the US debt limit by a deadline of next Tuesday.
The US Treasury has warned the government will run out of money to pay all its bills unless a $14.3tn (£8.7tn) borrowing limit is increased by then.
A key stumbling block remaind the insistence of the Republican-controlled House that raising the debt ceiling should be temporary and revisited early next year.
However, that would be in the middle of the 2012 election campaign.
President Obama has insisted the ceiling be increased sufficiently to push the issue beyond the 2012 vote.