WASHINGTON — The decision by Senate Democratic leaders last week to devote more time to winning Republican support for a health care overhaul has allowed President Obama to keep alive the possibility of bipartisanship on one of the most contentious issues on his agenda.

But Mr. Obama is under growing pressure to choose between wooing a small band of Republicans or struggling to rally his party to use its big majorities in Congress to get the job done. The bipartisanship exhibited in the passage of two other ambitious domestic programs that offer one historical backdrop for this debate — Social Security in 1935 and Medicare and Medicaid 30 years later — seems increasingly improbable in today’s Washington.

To some extent, achieving any kind of bipartisan accord seems almost a luxury given the difficulties Mr. Obama has had in corralling his own party behind a health care plan. After a sharp clash on Friday between different camps of Democrats on the health care bill, House staff members worked into the weekend in an effort to reach a compromise and bring a bill to the floor before recessing for the summer.

Even if he goes the bipartisan route and succeeds, the end result could be comparatively modest: Perhaps fewer than 10 Senate Republicans, and perhaps not even that many in the House, party officials said. Social Security, by contrast, passed in 1935 with the support of 16 of the 25 Republican senators and 81 of the 102 Republican representatives.

Still, ending partisan infighting was a central pledge Mr. Obama offered the nation from the earliest days of his candidacy. His aides have increasingly debated whether he should abide by it in the face of Republican resistance and liberal pressure not to concede on the principles of an overhaul plan, like a public plan to compete with private insurers. And how much are Democrats going to be willing to give up for what could be just a handful of Republican votes, and just the veneer of bipartisanship?

“If Republicans don’t make a genuine effort to negotiate to achieve health care reform, I certainly don’t think there’s a price to pay for doing it without them,” said Joel Benenson, the president’s pollster.

Should Mr. Obama abandon efforts to reach out to Republicans, he risks damaging his appeal among independent voters, who have a history of being put off by overt partisanship.

In addition, the go-it-alone course could cost Mr. Obama and, more important, Congressional Democrats political cover should the health care plan prove ineffective, unpopular or excessively costly before the 2010 or 2012 elections.

It could also set a polarizing pattern for the remaining three years of Mr. Obama’s first term, complicating his efforts to get through an ambitious agenda by forcing him to rely only on Democrats for votes.

“Technically he may be able to pass the bill in one of these big complex areas without bipartisan support, but it won’t be as good a product, and I suspect he’ll lose the support of the country in the process,” said Senator Lamar Alexander, the chairman of the Republican conference.

“There’s a huge price to be paid,” he added. “Bipartisanship is absolutely possible and it’s absolutely necessary, even when you have a Democratic president with huge majorities.”

No less important, a partisan vote could also undercut the political legitimacy of the effort itself. Social Security, Medicare and Medicaid were all passed with significant support from both parties, which is one of the reasons those programs have become such an accepted part of the country’s political landscape.

“Bipartisanship is a good thing in major welfare-state enterprises if they are to stick,” said David Mayhew, a professor of political science at Yale. “Otherwise, they may suffer legitimacy problems and come apart.”

That said, it is hardly clear that a bipartisan agreement on health care is even possible. A string of Congressional defeats has recast the Republican Party, leaving it smaller, more conservative and more combative.

“I wouldn’t even have hesitated two, four years ago when the numbers were so close: It would have been absolutely yes on bipartisanship,” said Senator Evan Bayh, Democrat of Indiana.

He said he still believed it was important, but added, “The Republicans are reduced to a core, so there aren’t that many pragmatists left to work things out.”

James A. Thurber, the director of the Center for Congressional and Presidential Studies at American University, said that 30 years ago, about one-third of Republicans in the House and Senate were moderate.

“In the last 30 years, we continually lost the middle, ideologically,” he said. “And the loss of the moderates makes it very difficult to get bipartisanship for major policy changes.”

The Senate Finance Committee right now offers the lone hope for the White House in its search for Republican support. That is also where the trade-off is particularly stark. It would mean giving up on some big principles, like a public plan to compete with private insurers, in return for what could be just a few Republican votes, a veneer of bipartisanship.

It is the prospect of that trade that has some Democrats worried and is another source of pressure for the White House.

“If they overstep the line in the negotiations to bring three or four Republicans along, there will be a reaction among Democrats unlike anything you’ll hear among Republicans,” Senator Christopher J. Dodd, Democrat of Connecticut, said Saturday. “There is a false assumption that anything you can work out with a handful of Republicans will be embraced by Democrats in the House, the Senate and across the country. That is totally wrong.”

David Axelrod, a senior adviser to Mr. Obama, said that while he thought it was important to make a strong effort to get bipartisan support, that would not trump passing legislation Mr. Obama wanted.

“Ultimately we are going to be measured by what we do, and not by the process,” Mr. Axelrod said. “Process can’t be more important than the outcome of the legislation.”

Republicans said this White House’s effort at bipartisanship had been one of symbols — presidential calls, invitations to the White House, regular tending by such high level officials as Mr. Axelrod and Rahm Emanuel, the chief of staff — rather than substance.

“We hear from them all the time,” Mr. Alexander said. “They said the right things. They are as cordial as you can be.”

But, Mr. Alexander said, the talk has not yet led to a serious effort to find a bipartisan solution. “They should at least try it. They haven’t tried it,” he said.

The last time Congress came close to achieving bipartisan agreement on a major piece of legislation was No Child Left Behind in 2001, though a significant number of Democrats voted for President George W. Bush’s tax cut in 2001.

Mr. Bayh said there was another powerful incentive for Democrats to try to work with Republicans on health care.