Conservative Republicans say House Speaker John Boehner does not have enough votes in his own party to pass the measure. But even if it were to pass in the House, Majority Leader Harry Reid said the measure stood no chance of passing the Senate.
The bill would raise the debt limit by $1 trillion while making cuts to federal spending of $1.2 trillion, reductions that conservatives say aren't enough.
The Congressional Budget Office ran the numbers and says it falls short by $150 billion. Boehner on Tuesday night rewrote that bill looking for more cuts, but it still may not be enough to appease his own House conservatives.
The measure also would establish a committee of lawmakers to recommend additional budget savings of $1.8 trillion, which would trigger an additional $1.6 trillion increase in the debt limit.
Many House conservatives have signed a pledge to vote against any debt ceiling increase unless it comes with much more dramatic deficit cutting measures.
"Speaker Boehner's plan is not a compromise, it was written for the tea party and not the American people," Reid said.
With conservatives unhappy, and if Democrats remain united against Boehner's plan, his margin of error is thin. There are 240 House Republicans. It will take 217 votes to pass the bill. That means Boehner can't lose more than 23 of his own party to succeed.
Congressman Jim Jordan (R-Ohio) says Boehner doesn't have the votes. The speaker himself acknowledged they're not there yet.
The vote originally scheduled for Wednesday is now set for Thursday. The deadline for Congress to raise the debt ceiling is Aug 2, one week away.
A Democratic plan in the Senate would extend the borrowing limit into 2013, but that plan is not expected to pass either.
The bitter stalemate could have far-reaching repercussions for the fragile U.S. economy as well as global markets. Stocks declined Tuesday as U.S. markets registered their nervousness over the Washington gridlock between President Barack Obama and Republicans.
With time running out, Americans are making their voices heard.
They crashed the websites of Boehner, Sen. Mitch McConnel and others. They clogged phone lines at Reid's office and at Capitol Hill, all because of a few simple words.
"If you want a balance approach to reducing the deficit, let your member of Congress know," Obama said in an address to the nation Monday night.
Many Americans say the deadlock over the debt is unacceptable.
"I wish the Republicans would grow up and do what they need to do," said Phyllis Tucker of Studio City.
Others say the president hasn't done enough.
"You wouldn't run a company the way you run our nation," said Sylmar resident Terry Neven.
On Twitter, New York journalism professor Jeff Jarvis expressed that frustration with the hashtag, "#F---YouWashington."
According to a Twitter tracking site, the hashtag had been used more than 20,000 times an hour since then.
"We can't allow the American people to become collateral damage to Washington's political warfare," Obama told the nation.
Boehner, in a rebuttal, said, "The president would not take yes for an answer."
The Associated Press contributed to this report.