President Obama and House Speaker John A. Boehner rushed Thursday to strike agreement on a far-reaching plan to reduce the national debt but faced a revolt from Democrats furious that the accord appeared to include no immediate provision to raise taxes.

With 12 days left until the Treasury begins to run short of cash, Obama and Boehner (R-Ohio) were still pursuing the most ambitious plan to restrain the national debt in at least 20 years. Talks focused on sharp cuts in agency spending and politically painful changes to cherished health and retirement programs aimed at saving roughly $3 trillion over the next decade.

More savings would be generated through an overhaul of the tax code that would lower personal and corporate income tax rates while eliminating or reducing an array of popular tax breaks, such as the deduction for home mortgage interest. But the talks envisioned no specific tax increases as part of legislation to lift the debt limit, and the tax rewrite would be postponed until next year.

Democrats reacted with outrage as word filtered to Capitol Hill, saying the emerging agreement appeared to violate their pledge not to cut Social Security and Medicare benefits as well as Obama’s promise not to make deep cuts in programs for the poor without extracting some tax concessions from the rich.

When “we heard these reports of these mega-trillion-dollar cuts with no revenues, it was like Mount Vesuvius. . . . Many of us were volcanic,” said Sen. Barbara A. Mikulski (D-Md.).

White House budget director Jacob J. Lew denied that a deal without taxes was in the works. “We’ve been clear revenues have to be part of any agreement,” he told reporters.

After a lunchtime meeting between Lew and Senate Democrats, Majority Leader Harry M. Reid (D-Nev.) made no attempt to hide his anger, telling reporters that his caucus would oppose the “potential agreement” because it appeared to include no clear guarantee of increased revenue.

“The president always talked about balance, that there had to be some fairness in this, that this can’t be all cuts. There has to be a balance. There has to be some revenue and cuts. My caucus agrees with that,” Reid said. “I hope that the president sticks with that. I’m confident that he will.”

Congressional and administration officials said the White House informed Democratic leaders about the talks after Obama met privately with Boehner and House Majority Leader Eric Cantor (R-Va.) late Wednesday. Congressional aides, speaking on the condition of anonymity to detail private discussions, said the White House acknowledged that the emerging agreement is “to the right of the Gang of Six” — a bipartisan Senate debt-reduction framework unveiled this week — and far removed from what Democrats have said would be acceptable.

The White House is seeking a trigger that would allow the Bush-era tax cuts to expire for the nation’s wealthiest households. Boehner has proposed repealing provisions of Obama’s health care law, including the requirement that all individuals purchase health insurance after 2014.

Obama summoned top Democratic leaders in both the House and the Senate back to the White House later Thursday for further discussions.

While Senate Democrats fumed, other Democratic officials familiar with the administration’s approach to the talks said the goal is still to reduce the debt in a balanced way that tackles both the tax code and rising entitlement spending. While the two sides are nowhere near an agreement, the officials said, they are focused on a two-part package. The first measure would raise the debt limit through 2013 and specify cuts to domestic agencies, including the Pentagon, over the next decade.

If both sides agree, that measure could also include some tax and entitlement changes, such as ending breaks for corporate jets, raising the Medicare eligibility age or changing the measure of inflation used to adjust Social Security benefits. However, the largest tax and entitlement changes are likely to be left until next year, the officials said, when policymakers will have more time to weigh the effects on taxpayers, program beneficiaries and the economy.

The officials said the toughest part of the negotiations has been finding common ground on the magnitude of those changes and the shape of a mechanism that would automatically cut spending or raise taxes if Congress fails to follow through. In any case, the officials said, no taxes would go up and no entitlement changes would take effect until at least 2013.

Before leaving for the White House on Thursday, Reid cut short debate on a GOP bill that would impose federal spending caps and send a constitutional amendment requiring balanced budgets to the states for ratification. Reid had considered extending debate into the weekend, but instead he angrily declared it was “perhaps some of the worst legislation in the history of the country” and set a final vote for Friday.

If the Obama-Boehner deal comes together, House Republicans would move the legislation first in their chamber, perhaps later next week, according to a senior Senate GOP aide. This move would short-circuit a previous effort by Reid and Senate Minority Leader Mitch McConnell (R-Ky.), who have been crafting a backup plan that would allow Obama to increase the federal debt limit himself unless a two-thirds majority in Congress objected.

Policymakers are racing to forge agreement on a plan to stabilize the soaring national debt before Aug. 2, when the Treasury will be unable to pay the nation’s bills without additional borrowing authority. Lawmakers in both parties are reluctant to raise the $14.3 trillion debt limit without a clear plan for restraining future borrowing. But they are running out of time to strike such a deal, draft legislation, submit it to congressional budget analysts and win the votes needed to push it through Congress.

Despite the loudly ticking clock, Obama and Boehner are trying to revive the “grand bargain” that eluded them earlier this month. Then it was Republicans, including Cantor and other conservatives, who raised objections, saying they were unwilling to trade tax increases of as much as $1 trillion over the next decade for deep spending cuts and significant changes to Social Security and Medicare.

Since then, with polls showing increasing public annoyance with GOP intransigence, Cantor has signaled that his views on a grand bargain are in flux. So Boehner restarted talks with the White House. The White House, in turn, according to congressional sources, dropped its demand for a big upfront concession from Republicans: an agreement to immediately extend tax cuts enacted under President George W. Bush for middle-class households, leaving cuts benefiting the wealthiest households to expire on schedule next year.

Democrats said this element of the deal would have given them leverage against Republicans to force a rewrite of the tax code that raises revenue. Republican leaders are insistent on extending tax cuts for the highest earners, including many entrepreneurs and business owners. If that part of the bargain were taken off the table, the aides said, Democrats see no guarantee that Republicans would actually agree to an overhaul of the tax code that raises revenue.

Democratic Senate leaders warned the Republican-controlled House, meanwhile, that time is running out for a comprehensive deal that would include raising the federal debt limit. They urged the House to remain in session and to ignore “extreme right-wing ideologues” who reject compromise.

A day after the White House signaled that Obama would accept a short-term hike in the debt ceiling if it gave lawmakers time to finalize a comprehensive deal, Reid condemned the House GOP leadership for reversing course on a plan to remain in session through the weekend and instead take Saturday and Sunday off.

Reid said it would present “a very bad picture” if House members leave town this weekend without a deal. He noted that, under congressional rules, a bill that involves revenue would have to start in the House, meaning a deal such as that sought by Obama and Boehner could not begin moving through Congress until next week.

In separate floor remarks, Sen. Charles E. Schumer (N.Y.), the third-ranking Democrat in the Senate, asked whether the United States would allow itself “to be driven into default and financial calamity by a small group of extreme right-wing ideologues in the House GOP.”

Charging that House Republicans are “becoming increasingly isolated,” Schumer urged them to seize a “life line” thrown to them by Grover Norquist, president of Americans for Tax Reform, who was quoted in a Washington Post editorial Thursday as telling the paper’s editors that the elimination of a tax cut or special-interest tax break would not necessarily amount to a tax increase.

However, Norquist backed away from the reported remarks Thursday, saying his influential group would oppose any move to allow the 2001 and 2003 tax cuts by the Bush administration to expire as currently scheduled. He asserted that expiration of the cuts would amount to a tax increase.

As the contentious budget talks dragged on, White House spokesman Jay Carney said Wednesday that Obama could accept an extension of the debt limit by “a few days” if it allowed a long-term deficit-reduction and debt-ceiling deal to work its way through Congress. Obama had pledged to veto any short-term measure to raise the debt ceiling.

Staff writer Felicia Sonmez contributed to this report.