House Republicans delayed a vote on their bill to lift the debt ceiling as they scrambled Tuesday night to rewrite the measure to ensure that accompanying spending cuts were large enough, according to three senior GOP aides.

The vote, originally scheduled for Wednesday, could now happen Thursday.

House members have just seven days to raise the debt ceiling before next Tuesday’s deadline, and the latest move came after budget analysts said the plan endorsed by Speaker John A. Boehner (R-Ohio) would only create $850 billion in government savings, rather than the sought-after $1.2 trillion.

Boehner had spent much of Tuesday furiously rallying support for his two-step plan to avert a potential default, even though Senate Majority Leader Harry M. Reid declared the proposal “dead on arrival” in his chamber and the White House issued a veto threat.

Senior lawmakers and aides continued negotiations aimed at finding a compromise between competing plans from Boehner and Reid (D-Nev.). But the two sides were still split over whether to hold multiple votes over the next eight months to lift the government’s debt limit or to have just one vote in the next few days that would extend the Treasury’s borrowing authority into 2013. Boehner’s plan calls for linking increases in the debt ceiling in two stages to about $3 trillion in spending cuts.

The White House expressed strong opposition to Boehner’s proposal Tuesday afternoon and threatened a veto, and Boehner also faced misgivings in his own party. About 10 House Republicans publicly declared opposition to his plan as too timid in its restraints on spending, and about nine more suggested they were leaning against the plan. Few, if any, Democrats were expected to support his plan, so the speaker could afford to lose only about two dozen of his 240 House Republicans.

Nevertheless, Reid made plans to kill off Boehner’s proposal in the event it landed in the Senate. “It’s dead on arrival if they get it out of the House,” Reid told reporters Tuesday after his own closed-door meeting of Senate Democrats.

Senate Minority Leader Mitch McConnell (R-Ky.), appearing immediately after Reid, denounced Reid’s plan to save $2.7 trillion in exchange for a commensurate elevation in the debt ceiling as “not a serious effort,” citing the Nevada Democrat’s accounting for $1 trillion in savings over the next decade through the drawdown of troops from Iraq and Afghanistan. Republicans said those were not real savings because they were already anticipated by the administration and lawmakers, even if government budget analysts officially score current budgets over 10-year periods.

This raised the stakes for the ongoing talks between Boehner and Reid as they negotiated a potentially decisive new path to a deal by an Aug. 2 deadline. The two men spoke Tuesday morning.

With a debt-limit deadline now a week away, the International Monetary Fund weighed in forcefully, warning of “serious spillovers” worldwide if the U.S. debt ceiling is not raised.

Responding to Obama’s appeal in a speech Monday night for Americans to contact their members of Congress to urge them to adopt his “balanced approach” to deficit reduction, callers flooded Capitol telephone circuits Tuesday morning, and several lawmakers’ Web sites — including Boehner’s — reportedly crashed Monday night as huge numbers of people tried to send them messages.

According to a new poll , 68 percent of Americans — including majorities across the political spectrum — now say lawmakers should compromise to strike a deal on the debt, up from 55 percent in a poll taken in April.

In his televised address, Obama called for a compromise that reduces the deficit through both spending cuts and increased revenue, while raising the debt ceiling in one step into 2013. Speaking minutes afterward, Boehner (R-Ohio) argued for a plan that would extend the debt ceiling initially for about six months and require another vote to lift it further in 2012. Obama has vowed to veto any such short-term extension, which ratings agencies have said might not be sufficient to avert a downgrading of the United States’ AAA credit rating.

Shrugging off Obama’s efforts to appeal directly to the public, Boehner pushed not only for a House vote Wednesday on his two-stage plan, but scheduled a second vote Thursday on an amendment to the Constitution requiring a balanced budget. A balanced-budget amendment is part of a GOP plan that was approved by the House last week but voted down in the Democratic-controlled Senate. Obama had pledged to veto any such plan that reached his desk.

The House GOP leadership team, often described as fractious, showed complete unity behind closed doors and in public Tuesday. House Majority Leader Eric Cantor (R-Va.) told Republicans he was “150 percent” behind Boehner and his plan, according to Republicans who attended Tuesday morning’s closed-door meeting. He told Republicans to “stop grumbling and whining and to come together as conservatives” to support the Boehner proposal.

House Majority Whip Kevin McCarthy (R-Calif.), the party’s vote counter, began his talk by showing a clip from the movie, “The Town”, trying to forge a sense of unity among the independent-minded caucus.

One character asks his friend: “I need your help. I can’t tell you what it is. You can never ask me about it later.”

“Whose car are we gonna take,” the character says.

After showing the clip, Rep. Allen West (R-Fla.), one of the most outspoken critics of leadership among the 87 freshmen, stood up to speak, according to GOP aides.

“I’m ready to drive the car,” West replied, surprising many Republicans by giving his full -throated support for the plan.

However, a leading conservative lawmaker, Rep. Jim Jordan (R-Ohio), said enough Republicans appear to oppose Boehner’s plan that it would not be able to pass the House on GOP support alone.

In a speech in New York before the Council on Foreign Relations, meanwhile, Christine Lagarde, the new managing director of the IMF, urged American officials to demonstrate the kind of “political courage” she said was shown by European leaders last week in a summit that agreed on new financing for Greece and gave greater powers to a regional bailout fund.

“On the debt ceiling, the clock is ticking, and clearly the issue needs to be resolved immediately,” Lagarde said. “Indeed, an adverse fiscal shock in the United States could have serious spillovers on the rest of the world.” She said a default or downgrading of U.S. debt “would be a very, very, very serious event, not just for the United States but for the global economy at large.”

Lagarde also urged caution in adopting large deficit-reduction measures, saying that “the impact is likely to be negative” in the short term. “Our research has found that a 1 percentage point cut in the deficit could lower growth by about one-half percentage point over two years,” she said. “This is why measures that are legislated now — but only reduce deficits in the future, when the recovery is more robust — would be particularly helpful.”

Staff writers Jon Cohen and Felicia Sonmez contributed to this report.