President Obama would consider a short-term measure aimed at raising the nation’s debt ceiling and avoiding a default by Aug. 2 if Congress agrees to a larger, long-term deficit-reduction and debt-ceiling deal and needs “a few days” to finalize the legislation, his spokesman said Wednesday.

With time running out for reaching such a deal, Obama called House and Senate Democratic leaders to a White House meeting Wednesday as he sought to shore up his party’s support for a compromise deficit-reduction plan that could help break a political impasse over the debt limit and avert a U.S. default.

Later, Obama was scheduled to confer at the White House with the top two House Republicans: Speaker John A. Boehner (Ohio) and Majority Leader Eric Cantor (Va.).

Obama has steadfastly refused to entertain proposals to temporarily lift the debt limit during tense negotiations with congressional leaders over the past several weeks. But with less than two weeks remaining before economists say the government would risk defaulting on its obligations if the debt ceiling were not raised, the administration appeared to recognize the time constraints that could prevent a larger “grand bargain” from being enacted.

“The president has been clear that he will not support a short-term extension of the debt ceiling,” White House spokesman Jay Carney said. But he added: “What we mean by that is we would not support a short-term extension absent an agreement to a larger deal. That’s not acceptable. Obviously, if both sides agree to something significant, we will support the measures needed to finalize the details of that.”

In response to questions, Carney said later, “But there is no extension without an agreement on something big — a firm, committed agreement on something big.”

Obama has continued to push for a larger deficit-reduction package that includes a mix of reduced spending and increased revenues through changes to the tax code. A bipartisan group of senators called the “Gang of Six” submitted a package that would reduce the deficit by $3.7 trillion, a proposal the administration hailed as a step in the right direction. Carney declined to talk about specifics of the proposal but said Obama was encouraged by the group’s approach.

Carney said Obama will not sign a series of short-term increases to the debt ceiling as stop-gap measures, which he said would “cast doubt” on the willingness of the United States to honor its obligations. He drew a distinction between such short-term measures and a “backup plan” to raise the debt ceiling in three phases extending more than a year and totaling about $2.5 trillion. This plan is being worked out between Senate Minority Leader Mitch McConnell (R-Ky.) and Senate Majority Leader Harry M. Reid (D-Nev.). Carney said Obama could sign such a fallback plan because, under it, the three phases would be guaranteed and the debt ceiling would be raised “into 2013.”

Carney said: “We are not wavering on the president’s absolute assertion that he won’t sign . . . a toll booth kind of series of provisions that temporarily or in a limited fashion raise the debt ceiling, and we have to relitigate this again and again and again.”

Obama took this position “not just because it’s unpleasant . . . but because it’s bad for the economy,” Carney said. “It sends the wrong signal to everyone around the globe about Washington’s capacity to deal with its fiscal issues. . . . If we send a signal from Washington that Washington works, that Washington can tackle big problems, that will have significantly positive impact around the globe.”

With Republicans accusing Obama of backing away from his earlier vow to veto a short-term measure, Carney later elaborated on his position in a written statement.

“The president does not support a short-term extension of the debt limit, period,” Carney said. “The only exception to that is in the event that both sides reach a deal on a long-term extension of the debt limit plus significant deficit reduction, and we needed a very short-term extension (like a few days) to allow a bit of extra time for a bill to work its way through the legislative process.”

Faced with the looming deadline for raising the ceiling on federal borrowing, Obama invited Senate Majority Leader Reid, House Minority Leader Nancy Pelosi (D-Calif.) and their deputies to the White House a day after the president and lawmakers in both parties latched on to a new strategy that calls for $3.7 trillion in spending cuts over the next decade.

In announcing the 2:50 p.m. meeting, Carney told reporters that while “Republicans need to be willing to compromise” on a deficit-reduction plan, “the same is true for Democrats.” He said Obama “is willing to take political heat” in arguing to Democrats that they must make “tough choices” on spending cuts now so that vital investments in future economic growth can continue.

Pelosi reacted positively to the emerging plan Wednesday, telling reporters, “It has some good principles in it.” But Reid, who has been working on a more limited proposal to raise the debt ceiling, so far has withheld public backing for the new proposal.

The proposal, crafted by a bipartisan group of senators known as the “Gang of Six,” calls for $500 billion in immediate savings and requires lawmakers in the coming months to cut agency spending, overhaul Social Security and Medicare, and rewrite the tax code to generate more than $1 trillion in fresh revenue.

In the works since January, the plan became public Tuesday, just as it was becoming apparent that the leading option for raising the federal debt limit faces bleak prospects in the House. With the Treasury expected to start running out of cash in two weeks, House Republicans are openly hostile to a Senate-led plan that would authorize additional borrowing but kick the hardest decisions — such as whether to raise taxes or cut entitlement programs — to a special legislative panel.

The Gang of Six framework, by contrast, would force lawmakers to make some of those tough decisions now. The urgency of the situation was underscored Tuesday when a major credit-rating company said it could downgrade five states, including Maryland and Virginia, in addition to the federal government if the United States defaults on its obligations.

Carney stressed that urgency again Wednesday. “Obviously, time is running short,” he said. But he said there is “still time to do something significant” along the lines of the Gang of Six plan “if all parties are willing to compromise.”

As many policymakers were turning their attention to the new strategy, the Republican-controlled House forged ahead Tuesday with another approach to the debt crisis, voting to sharply cut spending and tie an increase in the debt limit to the eventual adoption of a balanced-budget amendment. The measure is unlikely to pass the Senate, and Obama has promised to veto the bill if it does.

The new plan emerging from the Senate may have better prospects. House Speaker John A. Boehner (R-Ohio) said through a spokesman that the Gang of Six plan “shares many similarities with” the far-reaching strategy he had been pursuing with Obama this month but abandoned amid GOP opposition to fresh revenue. The president agreed, and he hailed Republican openness to a plan that includes new taxes as “a very significant step.”

“It’s time to get down to the business of actually solving this problem. And I think we now are seeing the potential for a bipartisan consensus around what that would take,” Obama told reporters during a quick appearance in the White House briefing room.

Neither Obama nor Boehner embraced the specific details of the Gang of Six proposal, and it was not immediately clear how the strategy might influence debt-limit negotiations. House Majority Leader Eric Cantor (R-Va.) said in a statement that the plan contains “some constructive ideas for dealing with our debt,” but he objected to the revenue goals, arguing that “a tax increase is the wrong policy to pursue with so many Americans out of work.”

Senate leaders, who have long been skeptical of the Gang of Six were notably cool to the proposal. Minority Leader Mitch McConnell (R-Ky.) offered no opinion, while Reid highlighted the procedural obstacles to shifting legislative strategies so late in the game.

Reid, who has been adamant in his opposition to cutting Medicare and Social Security benefits as part of the debt-limit negotiations, acknowledged that he does not support the proposal.

“For me to say I love this bill that other people have worked on for months and months, I can’t do that,” Reid told reporters, adding, “Remember, we have only 13 days.”

The ticking clock is a major impediment to pursuing the Gang of Six strategy, which has yet to be drafted in legislative form or examined by congressional budget analysts. Opponents ripped into the sketchy details handed out at a morning briefing attended by about half the Senate, arguing that printed summaries identify nowhere near $3.7 trillion in savings.

Still, the plan was attracting interest among House Republicans eager for bold action to restrain borrowing. Rep. Steven C. LaTourette (R-Ohio), a close Boehner ally, said, “Anything that moves toward the grand bargain that the speaker and the president have been working on is great.”

And freshman Rep. Charles F. Bass (R-N.H.) called the proposal “a move in the right direction.”

“There’s tax reform, there’s significant spending reduction, and there’s also a debt-ceiling increase,” Bass said. “This is a positive development, and I’m going to be very open-minded about it.”

In the Senate, the plan received a warm response, both during the invitation-only morning session and during separate luncheon briefings for Democrats and Republicans. Sen. Lamar Alexander (Tenn.), the No. 3 Senate Republican, offered strong support. And Sen. Tom Coburn (R-Okla.), a leader in the GOP on budget issues, backed the plan as well, after dropping out of the Gang of Six in mid-May.

“There was palpable relief from folks in that room this morning. Like they were saying, ‘Here’s something we can actually be for,’ ” said Sen. Mark R. Warner (D-Va.), a Gang of Six member who has relentlessly pressed his colleagues to reach consensus.

Now that the plan is in the open, Warner said, “it’s put-up-or-shut-up time — for all of us.”

The Gang of Six was formed in the wake of Obama’s fiscal commission, an 18-member panel whose ideas sparked broad interest. Reluctant to let that effort die, Warner and Sen. Saxby Chambliss (R-Ga.) joined forces with four senators who served on the commission to try to draft legislation to bring its recommendations to a vote.

The newly released framework relies heavily on the fiscal commission’s work, calling for deep cuts at government agencies, including the Pentagon; significant reductions to Medicare and Medicaid; and a plan to make Social Security solvent.

It also calls for raising more than $1 trillion over the next decade by reducing a variety of popular tax breaks and deductions, including breaks for home mortgage interest and employer-provided health care. While some of those savings would be dedicated to debt reduction, the rest would go toward lowering tax rates for everyone, with top individual and corporate rates dropping to at least 29 percent, down from 35 percent.

The work on taxes and entitlements would be done largely by existing legislative committees that would be given targets for achieving savings over the next six months. If any committees failed to act, 10 senators — five from each party — could step in to offer their own proposal.

Senate Budget Committee Chairman Kent Conrad (D-N.D.), a member of the group, said Senate leaders were looking at ways to add Gang of Six goals to legislation already in development to raise the debt ceiling.

But “the first test,” Conrad said, is getting 60 senators to sign a letter saying, “This is a direction that deserves support.”

The emergence of the Gang of Six proposal overshadowed political sparring in the House on Tuesday over a GOP plan to cut spending by $111 billion next year, impose strict caps over the next decade and raise the $14.3 trillion debt limit only after Congress approves a constitutional amendment requiring a balanced budget.

That measure, which passed 234 to 190, has virtually no chance of approval in the Senate. But lawmakers in both parties said the debate could prove useful in the quest for a final deal because it allows conservatives to go on record with their preferred plan before considering a less palatable alternative.

“I think there’s recognition that it’s not going to be signed into law,” Bass said of the measure known as “cut, cap, balance.” “But it’s an important step [that] allows people like me, who do support a balanced-budget amendment, an opportunity to vote on that.”

Staff writers Rosalind S. Helderman and Paul Kane contributed to this report.