WASHINGTON — President Barack Obama, plunging into the rancorous struggle over America’s mountainous debt, will draw sharp differences with Republicans Wednesday over how to conquer trillions of dollars in spending while somehow working out a compromise to raise some taxes and trim a cherished program like Medicare.

Obama’s speech will set a new long-term deficit-reduction goal and establish a dramatically different vision from a major Republican proposal that aims to cut more than $5 trillion over the next decade, officials said Monday.

Details of Obama’s plan are being closely held so far, but the deficit-cutting target probably will fall between the $1.1 trillion he proposed in his 2012 budget proposal and the $4 trillion that a fiscal commission he appointed recommended in December.

The speech is intended as a declaration of Obama’s commitment to seriously tame the deficit while outlining his long-term budget principles — key components of his campaign for re-election in 2012.

After gingerly avoiding any discussion until now of cuts in the government’s massive benefit programs for the elderly and poor, Obama will acknowledge a need to reduce spending on Medicare and Medicaid while at the same time tackling defense spending and calling for increased taxes on the wealthy, White House officials said.

If that sounds like a reprise of last week’s budget fight that barely avoided a government shutdown, it isn’t. The stakes are far higher, the political risks greater and the goals more ambitious. At issue are long-term budget deficits and a $14.3 trillion national debt that many say could threaten the nation’s economy.

The cuts accomplished last week were for $38.5 billion over the next six months; the cuts envisioned now are for trillions of dollars over the next 10 years.

Obama’s speech, to be delivered at George Washington University, comes as Congress readies for a fierce fight over raising the nation’s debt limit. Republicans have vowed to use that vote as leverage to extract greater budget discipline from the Democrats and the president.

Setting the terms of the debate and the likely brinkmanship to follow, White House spokesman Jay Carney said on Monday: “What I’m saying is that we support a clean piece of legislation to raise the debt ceiling. … We cannot play chicken with the economy in this way.”

The president’s speech also comes amid liberal apprehension over recent Obama spending concessions and a desire among some Democrats to make proposed GOP cuts in Medicare a 2012 election issue. 

House Republicans, led by the chairman of the House Budget Committee, Paul Ryan, last week unveiled a plan that would cut $5.8 trillion over 10 years with a major restructuring of the nation’s signature health care programs for the elderly and the poor.

Meanwhile, six senators have formed a bipartisan group to work on their own plan to rein in long-term deficits by making changes to Medicare and Medicaid and examining a fundamental overhaul of the tax system that would yield additional revenue.

Obama is expected to concede a need for overhauling Medicare and Medicaid and to even make adjustments to Social Security, always considered politically risky territory. But he will distinguish his plan from the Republican budget, which would shrink Medicare by shifting the program to private insurers and send block grants to states to pay for Medicaid, the health care program for the poor.

Unlike the Republican plan, Obama is also expected to call for cuts in defense spending and for tax hikes, repeating his 2012 budget plan to increase Bush era tax rates for families making more than $250,000. Obama shelved that plan in a budget compromise with Republicans.

The Republican plan, on the other hand, would make the Bush-era tax cuts permanent.

The debate over Medicare and Medicaid may not be resolved before the 2012 election, potentially making it the defining element of the presidential campaign. The weight of the debt has emerged as a powerful issue with independent voters, but both parties in the past have also used the fear of reduced benefits to motivate older votes.

The contrast the White House would like to pitch to the public is that Obama would help reduce the deficit by increasing taxes on the rich, while Republicans would pay for their tax cuts for the wealthy by making seniors pay more for their Medicare.

But now that Obama plans to propose his own changes in health care entitlements or Social Security, some of his own supporters are wary. They argue that the president ceded too much ground when he cut a tax deal with Republicans last December and in yielding spending cuts last week.

“I want to have confidence, but I’ve got to see something,” said Barbara Kennelly, a former Democratic congresswoman and president of the National Committee to Preserve Social Security and Medicare, an advocacy group. “They can’t continue to give in.”

Many liberals say Obama has not been a strong bargainer.

“Their weakness in getting the most out of negotiations is their strategic belief that they don’t want to be seen as fighting, they want to appear above the fray and beyond partisanship,” said Lawrence Mishel, president of the labor-leaning Economic Policy Institute. “They also believe that they shouldn’t get out there on a position where they may not succeed. These are characteristics that make for a weak negotiator.”

Republicans on Monday said Obama’s speech was overdue.

“I’m anxious to hear what the president has to say,“ House Speaker John Boehner said on Fox News.

“We’ve been waiting for months for the president to enter into this debate with us. I can tell you that privately I’ve encouraged the president: ‘Mr. President, lock arms with me, let’s jump out of the boat together. We have to deal with this, this is the moment in time that we’ve been given to address the problems.

“Forget the next election, forget the next poll that’s going to come out. It’s time to do the right thing for the country.’”

The speech is expected to affirm Obama’s stand on the spending he is not willing to cut, chiefly in the areas of education, energy, infrastructure, research and innovation. On Medicare, the federal insurance program for senior citizens, the president is expected to explain his case for cost savings without putting “all the burden on seniors,” as his senior adviser David Plouffe put it.

In choosing to wait until now, White House officials have looked at past precedents, including

President George W. Bush’s plan to partially privatize Social Security, and have seen the pitfalls of staking out major policy initiatives early that then come undone in Washington’s combative environment.

They also didn’t wish to confuse the recent debate over this year’s budget with the larger, more demanding undertaking of tackling the nation’s debt.