After spending months on the sidelines as Republicans laid out their plans, Mr. Obama jumped in to present an alternative and a philosophical rebuttal to the conservative approach that will reach the House floor on Friday. Republican leaders were working Wednesday to round up votes for that measure and one to finance the government for the rest of the fiscal year.

Mr. Obama said his proposal would cut federal budget deficits by a cumulative $4 trillion over 12 years, compared with a deficit reduction of $4.4 trillion over 10 years in the Republican plan. But the president said he would use starkly different means, rejecting the fundamental changes to Medicare and Medicaid proposed by Republicans and relying in part on tax increases on affluent Americans.

The president framed his proposal as a balanced alternative to the Republican plan, setting the stage for a debate that will consume Washington in coming weeks, as the administration faces off with Congress over raising the national debt ceiling, and into next year, as the president runs for re-election.

Mr. Obama named Vice President Joseph R. Biden Jr. to lead the negotiations with Congress, which the administration hopes will produce the outlines of a deal by the end of June, though a detailed agreement might have to await the outcome of the 2012 election. Mr. Biden played a similar role in talks that averted a government shutdown at the 11th hour, over issues far less thorny than those on the table now.

In a 44-minute speech to an audience at George Washington University that included Representative Paul D. Ryan of Wisconsin, the author of the Republican plan, Mr. Obama was often combative and partisan, saying the Republican approach would hurt the elderly by driving up the cost of medical care, deprive millions of health insurance and starve the nation of investments in its future.

“These are the kind of cuts that tells us we can’t afford the America that I believe in,” he said. “I believe it paints a vision of our future that’s deeply pessimistic.”

“There’s nothing serious about a plan that claims to reduce the deficit by spending a trillion dollars on tax cuts for millionaires and billionaires,” the president continued, as Mr. Ryan sat stone faced. “There’s nothing courageous about asking for sacrifice from those who can least afford it and don’t have any clout on Capitol Hill.”

Yet Mr. Obama acknowledged that the rising medical costs and the mounting debt required action. And he warned Democrats that his administration would have to cut cherished programs and strictly limit the growth of Medicare and Medicaid. “If we truly believe in a progressive vision of our society,” he said, “we have the obligation to prove that we can afford our commitments.”

Mr. Obama said he would meet his $4 trillion deficit-reduction target by cutting spending across a range of government programs, from farm subsidies to federal pension insurance.

He called for cutting $400 billion more in military spending — twice what his defense secretary, Robert M. Gates, told Congress was the largest cut he could recommend.

In a sign of the tensions the plan may cause within the administration, officials at the Pentagon said Mr. Gates was not told of Mr. Obama’s proposal until Tuesday. In a statement, a Pentagon spokesman, Geoff Morrell, said that “further significant defense cuts” would reduce the military’s capability. “It is important that any reduction in funding be shaped by strategy and policy choices, and not be a budget math exercise,” Mr. Morrell said.

Republicans criticized the plan, both for the cuts in military spending and for what they said was an overall lack of detail.

“Republicans, led by Chairman Ryan, have set the bar with a jobs budget that puts us on a path to paying down the debt and preserves Medicare and Medicaid for the future,” Speaker John A. Boehner said in a statement. “This afternoon, I didn’t hear a plan to match it from the president.”

Mr. Boehner repeated a threat to refuse to raise the $14.3 trillion ceiling on the national debt, which the government is likely to breach in early July, unless the administration agrees to rein in spending and deficits. The administration has sought to keep the debt ceiling issue separate from the broader budget debate, and Mr. Obama addressed it only indirectly on Wednesday.

“If our creditors start worrying that we may be unable to pay back our debts,” Mr. Obama said, “that could drive up interest rates for everyone.”

Still, in what some analysts said was a gesture to Republicans, Mr. Obama said his plan would contain a trigger to require across-the-board spending cuts if, by 2014, the federal debt was still projected to be rising as a percentage of the total economy.

The trigger would apply not only to spending but also to what the administration calls “tax expenditures” — essentially payments to taxpayers for deductions for charitable donations or home mortgages.

The use of the phrase “tax expenditures” allows the administration to lump tax-related issues into the spending category. Mr. Obama was more direct in his call for allowing the Bush-era tax cuts for higher-income Americans to expire in 2012.

The president agreed to extend the cuts last December, as part of a budget deal with the newly elected Republican majority in the House. Now, with the economy getting back on its feet, Mr. Obama attacked the demand by Republicans to make the lower tax rates permanent as emblematic of their plan to enrich the wealthy on the backs of the elderly and poor.

“They want to give people like me a $200,000 tax cut that’s paid for by asking 30 seniors to each pay $6,000 more in health costs? That’s not right, and it’s not going to happen as long as I am president,” Mr. Obama said, his only line that drew applause.

While Mr. Obama’s plan does not detail specific cuts, analysts said it offered enough detail to set off a substantive debate with Republicans. Some said the proposal for capping the annual cost increase in Medicare and Medicaid to just above the economic growth rate was surprisingly conservative. Others said they were pleased that Mr. Obama had called for overhauling Social Security, even if he was vague and said it was not a leading culprit for the deficit.

“It looks like Ryan smoked him out, so to speak,” said Rudolph G. Penner, a senior fellow at the Urban Institute.

Mr. Penner said Mr. Obama’s plan hewed closely to the recommendations of his commission on deficit reduction. Mr. Obama did not explicitly endorse those recommendations when the commission submitted its report in December — a decision that fueled criticism from Republicans and some Democrats that he was not facing up to the tough choices in the budget debate.

The co-chairmen of that commission — Erskine B. Bowles, who was a chief of a staff to President Bill Clinton, and former Senator Alan K. Simpson — were in the audience Wednesday, along with Mr. Biden. At one point, Mr. Biden appeared to nod off, closing his eyes for 30 seconds.

Jackie Calmes, John Harwood and Thom Shanker contributed reporting.

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