WASHINGTON - Stung by revelations that his plan would cut spending less than advertised, House Speaker John Boehner on Tuesday postponed a vote on a debt-ceiling measure that was already running into opposition from tea party conservatives. The move came just a week before an Aug. 2 deadline for staving off the potential financial chaos of the nation's first-ever default.

With time running short, the speaker promised to quickly rewrite his debt-ceiling legislation after budget officials said it would cut spending by less than $1 trillion over the coming decade instead of the promised $1.2 trillion. The vote originally scheduled for Wednesday is now set for Thursday. That may give Boehner more time to hunt for votes, but it gives Congress and the White House even less time for maneuvering.

Meanwhile, public head-butting between Democratic President Barack Obama and the Republicans showed no sign of easing. The White House declared Obama would veto the Boehner bill, even if it somehow got through the House and the Democratic-controlled Senate.

For all that, it was the tea party-backed members of Boehner's own party who continued to vex him and heavily influence the debt and deficit negotiating terms - not to mention his chances of holding on to the speakership.

Their adamant opposition to any tax increases forced Boehner to back away from a "grand bargain" with Obama that might have made dramatic cuts in government spending. Yet when Boehner turned this week to a more modest cost-cutting plan, with no tax increases, many conservatives balked again. They said the proposal lacked the more potent tools they seek, such as a constitutional mandate for balanced budgets.

Rep. Jim Jordan of Ohio, chairman of a large group of conservative Republicans, sent a tremor through the Capitol Tuesday when he said he doubted Boehner had enough support to pass his plan. The Boehner bill would provide an immediate debt ceiling increase but would require further action before the 2012 elections.

Obama strongly opposes that last requirement, arguing that it would reopen the delicate and crucial debt discussions to unending political pressure during next year's campaigns.

The president supports a separate bill, pushed by Majority Leader Harry Reid in the Democratic-controlled Senate, that would raise the debt ceiling enough to tide the government over through next year - and the elections.

Boehner wasn't helped when presidential candidate Tim Pawlenty and the groups Tea Party Patriots and Tea Party Express criticized his plan. A worse blow came when a congressional analysis said his plan would produce smaller savings than originally promised. Of particular embarrassment was a Congressional Budget office finding that Boehner's measure would cut the deficit by just $1 billion next year.

Boehner's office said it would rewrite the legislation to make sure the spending cuts exceed the amount the debt limit would be raised. Adding a political touch, it accused the Democrats of declining to put forward specifics subject to the same sort of review.

Earlier, responding to the conservative Republican opposition, Boehner quickly went on Rush Limbaugh's radio show, then he began one-on-one chats with wavering Republicans on the House floor during midday roll call votes.

"He has to convince a few people," Rep. Tom Petri, R-Wis., observed dryly from a doorway.

A serious, almost dire urgency ran through Boehner's efforts. The clock was ticking down to next Tuesday's deadline to continue the government's borrowing powers and avert possible defaults on U.S. loans.

Congressional veterans say a final-hour bargain can't be reached until both parties irrefutably prove to themselves and the public that neither the Democrats' top goals nor the Republicans' can be reached in the divided Congress.

Moreover, Boehner's grasp on the speakership could be weakened if he fails to pass the debt-ceiling plan that bears his name. Assuming no more than five Democrats support the measure - the same number that backed a GOP balanced-budget bill last week - Boehner can afford to lose no more than 28 of the House's 240 Republicans.

His allies predicted he'll make it, and Boehner got a vocal endorsement from his sometimes rival, Majority Leader Eric Cantor, R-Va. But holdouts were not limited to the much-discussed freshman class, elected in the tea party-fueled 2010 elections.

"He can't get my vote because I felt like that, for long-term solutions to this problem, all these promises we make in cutting spending never seem to occur," said Rep. Phil Gingrey, R-Ga. " I've been here nine years and I've never seen it happen yet."

Six-term Rep. Jeff Flake of Arizona, a long-time critic of deficit spending, said he also was leaning against Boehner's bill even though he knows a tougher measure cannot be enacted. "Obviously you have to weigh that against passing something that just doesn't solve the problem," Flake said.

Major business groups weighed in. The U.S. Chamber of Commerce urged support of Boehner's bill, while the conservative Club for Growth denounced it as too weak.

While Boehner searched for votes, some Americans seemed to edge closer to notion that the Aug. 2 deadline might pass without a solution. The stock market fell again, although not dramatically. California planned to borrow about $5 billion from private investors as a hedge against a possible federal government default.

The White House spoke with veterans groups about what might happen to vets' benefits if a deal isn't reached. Obama has said he can't guarantee Social Security checks and payments to veterans and the disabled would go out on schedule.

The Senate worked on other issues, waiting to see if Boehner's bill would pass the House and come its way. Reid, D-Nev., said the Boehner bill could not pass his chamber.

Reid has his own plan. Like Boehner's, it would identify about $1.2 trillion in spending cuts to the day-to-day operating budgets of government agencies. Reid's proposal, however, would require only one congressional vote to raise the debt ceiling before the 2012 elections. And it counts an extra $1 trillion in savings from winding down the wars in Iraq and Afghanistan.

Both proposals would create a bipartisan congressional commission to identify further deficit reductions, especially in major health care programs such as Medicare and Medicaid.

For seven months, tea party-backed House members - freshmen and veterans alike -have rewritten congressional traditions. Speakers typically can twist arms, offer favors and issue veiled threats to round up the needed support on tough votes. It's possible Boehner will be able to do so on the debt-ceiling matter.

But many tea party activists abhor political compromise. They insist that their elected officials stand on principle, regardless of the consequences.

"A lot of the tea party guys owe certain support groups," said Rep. Walter Jones Jr., R-N.C. He said he had not decided how to vote on Boehner's bill.

Freshman Rep. Trey Gowdy, R-S.C., bristles at the notion that tea party-influenced newcomers are sheep-like ideologues willing to risk default. "We're not a bunch of knuckle-dragging, mouth-breathing Neanderthals," Gowdy said. "We're interested in answering what we perceive to be the mandate, which is to stop the spending and change the way Washington handles money."

Gowdy said he was leaning against Boehner's proposal.

But freshman Rep. Allen West, R-Fla., a tea party favorite, felt otherwise.

"This Boehner plan, does it have everything that I want in it?" West said. "Absolutely not. It is the 70-75 percent plan that we can go forward with."

Petri, a 33-year House veteran, said Boehner may need the votes of 35 to 40 Democrats, which Democratic leaders say is impossible.

Asked how Boehner will get out of his predicament, Petri paused and said: "When I think of it, I'll give him a call."

Associated Press writers Laurie Kellman, Jim Abrams, Steven Ohlemacher, Alan Fram, Donna Cassata and Larry Margasak contributed to this report.