WASHINGTON — Passage of the health care legislation challenges the heart of the Republicans’ strategy this year: To present a unified opposition to big Democratic ideas, in this case expressed in a stream of bristling anger and occasional mischaracterizations of what the bill would do.

President Obama will sign the bill Tuesday, although with the support of only Democrats. An additional package of amendments to remove some of the more politically problematic provisions is likely to become law within weeks.

In political terms, Republicans face strong crosscurrents. Polls suggest that a sizable part of the nation is unenthusiastic about the bill or opposed to it. Conservatives see it as a strike at the heart of their small-government principles, helping to explain why Republicans are optimistic that they will make gains in the midterm elections in November.

“There is no downside for Republicans,” Michael Steele, the Republican National Committee chairman, said Monday in an interview. “Only for Americans.”

But at the same time, many provisions of the bill that go into effect this year — like curbs on insurance companies denying coverage for pre-existing conditions, or the expansion of prescription drug coverage for the elderly — are broadly popular with the public. The more contentious ones, including the mandate for the uninsured to obtain coverage, do not take effect for years.

And in a week when Democrats are celebrating the passage of a historic piece of legislation, Republicans find themselves again being portrayed as the party of no, associated with being on the losing side of an often acrid debate and failing to offer a persuasive alternative agenda.

David Frum, a fellow at the American Enterprise Institute, the conservative research organization, said Republicans had tried to defeat the bill to undermine Mr. Obama politically, but in the process had given up a chance of influencing a huge bill. Mr. Frum said his party’s stance sowed doubts with the public about its ideas and leadership credentials, and ultimately failed in a way that expanded Mr. Obama’s power.

“The political imperative crowded out the policy imperative,” Mr. Frum said. “And the Republicans have now lost both.”

“Politically, I get the ‘let’s trip up the other side, make them fail’ strategy,” he said. “But what’s more important, to win extra seats or to shape the most important piece of social legislation since the 1960s? It was a go-for-all-the-marbles approach. Unless they produced an absolute failure for Mr. Obama, there wasn’t going to be any political benefit.”

Republicans also face the question of what happens if the health care bill does not create the cataclysm that they warned of during the many months of debate. Closing out the floor debate on Sunday night, the House Republican leader, Representative John A. Boehner of Ohio, warned that the legislation would be “the last straw for the American people.” Representative Marsha Blackburn, Republican of Tennessee, proclaimed several hours earlier, “Freedom dies a little bit today.”

Yet there are elements of the bill, particularly in regulating insurers, that could well prove broadly popular, and it could be years before anyone knows whether the legislation will have big effects on health care quality and the nation’s fiscal condition. Indeed, most Americans with insurance are unlikely to see any immediate change in their coverage, and several Republicans warned that the party could pay a price for that.

“When our core group discover that this thing is not as catastrophic as advertised, they are going to be less energized than they are right now,” Mr. Frum said.

He warned that the energy Republicans were finding now among base voters would fade.

The head of the Democratic Senatorial Campaign Committee, Senator Robert Menendez of New Jersey, offered a similar argument. “When this bill goes into effect, and none of the things Republicans warned about begin to happen — none of the death panels, none of the government takeover, none of the socialism — Republicans will have no credibility,” Mr. Menendez said.

The final deliberations, which drew protesters from across the country, including many Tea Party activists, cast an angry tone to the proceedings that also stirred concern among some Republicans. Some Democratic lawmakers said they had been taunted with racial epithets and homophobic slurs as they walked into the Capitol over the weekend to vote. Representative Randy Neugebauer, Republican of Texas, shouted out “baby-killer” on the House floor when Representative Bart Stupak of Michigan, one of the most fervent Democratic opponents of abortion in the House, outlined a deal he had worked out with the White House, which he said assured that the health care bill would not finance abortions.

Republican leaders dismissed any suggestion that the bill would hurt the party over the long term.

“Someone at Harvard or in San Francisco might think that, but not the rest of the country,” said Senator Lamar Alexander, Republican of Tennessee.

Mr. Alexander said Democrats would soon find themselves saddled with blame by Americans whenever they ran into a problem with an insurance company, even though Democrats have made a point of criticizing the insurance industry in the debate and asserting that without legislation the nation faced never-ending increases in premiums that would make health coverage less and less affordable.

“Insurance premiums are going to go up normally, and millions of Americans are going to experience higher premiums,” Mr. Alexander said. “All this is going to be coming, and the health care bill is going to get blamed for a lot of it.”

The bill has energized the Republican base in a way that could produce a spike of contributions and increase voter turnout.

But Mr. Menendez said that he was advising Democratic Senate candidates to challenge opponents about whether they would vote to repeal the bill — particularly, an expansion of prescription drug benefits for the elderly or requirements that insurance companies not deny coverage based on pre-existing conditions.

“We will challenge them,” he said. “What parts of this bill do you want to repeal?”

Gov. Haley Barbour, the head of the Republican Governors Association, said he believed that the bill was so unpopular that that line of political attack would not work.

“I would be for repealing the law,” Mr. Barbour said. “I would be for something better. There’s nobody that argues we don’t need health care reform. The argument is whether it’s good reform or bad reform.”