WASHINGTON — The White House and Democratic Congressional leaders, scrambling for a backup plan to rescue their health care legislation if Republicans win the special election in Massachusetts on Tuesday, are preparing to ask House Democrats to approve the Senate version of the bill, which would send the measure directly to President Obama for his signature.

A victory by the Republican, Scott Brown, in Massachusetts, would deny Democrats the 60th vote they need in the Senate to surmount Republican filibusters and advance the health legislation. And with the race too close to call, Democrats are mulling several options to save the bill, which could be a major factor in how they fare in this year’s midterm elections.

Some Democrats suggested that even if their candidate, Martha Coakley, eked out a narrow victory on Tuesday, they might need to ask House Democrats to speed the legislation to the president’s desk, especially if lawmakers who previously supported the bill begin to waver as they consider the political implications of a tough re-election cycle. It is unclear if rank-and-file Democrats would go along.

Even as Democratic leaders pondered their contingency plans, the House speaker, Nancy Pelosi, insisted that the health care legislation would move forward one way or another, though she acknowledged that Tuesday’s results could force a tactical shift.

“Certainly the dynamic will change depending on what happens in Massachusetts,” Ms. Pelosi told reporters in California on Monday. “Just the question of how we would proceed. But it doesn’t mean we won’t have a health care bill.”

“Let’s remove all doubt,” she added. “We will have health care one way or another.”

Still, some lawmakers, Congressional aides and lobbyists described numerous obstacles to the House’s approving the Senate-passed bill.

House Democrats have voiced a number of complaints with the Senate measure, and top White House officials and Congressional leaders have struggled to bridge differences between the two bills. And despite promises by Mr. Obama and Congressional leaders to add those hard-fought agreements and other changes later, there would be no guarantees.

In an interview on Monday, Representative Bart Stupak, Democrat of Michigan, who opposes the Senate bill because of provisions related to insurance coverage of abortions, said: “House members will not vote for the Senate bill. There’s no interest in that.”

When the idea was suggested at a meeting of the House Democratic Caucus last week, Mr. Stupak said, “It went over like a lead balloon.”

“Why would any House member vote for the Senate bill, which is loaded with special-interest provisions for certain states?” Mr. Stupak asked. “That’s not health care.”

In addition to his complaints about the abortion provisions, Mr. Stupak said the Senate bill does not do enough to improve the quality of health care, and it preserves the federal antitrust exemption for health insurance, which would be repealed under the House bill.

Officials at both ends of Pennsylvania Avenue emphasized that the backup plan was hypothetical, and that they hoped it would never be needed.

Many Democrats, eager to exude confidence, declined to comment publicly on the possibility of a Plan B. But Republicans said they expected Democrats to do whatever necessary to get the bill through.

“They are going to try every way, shape and form to shove this bill down the throats of the American people,” the House Republican leader, Representative John A. Boehner of Ohio, said in a radio interview on Monday.

Convincing House Democrats to adopt the bill approved by the Senate on Christmas Eve would obviate the need for an additional Senate vote. Although there would probably be enough time for Democrats to rush a bill through the Senate before Mr. Brown was sworn in, Democratic leaders have essentially ruled that out as a politically perilous option that could risk a serious public relations problem.

But asking House Democrats to adopt the Senate bill is itself the sort of high-risk audible that a coach calls only when the clock has run out and the entire season is on the line. Agreements that had been carefully forged over the last few days to bridge differences between the two bills would essentially be out the window.

The White House and labor unions, for instance, reached a tentative deal last week on an excise tax on high-priced, employer-sponsored insurance plans. Labor groups, an important segment of the Democratic Party’s base, strongly opposed the version of the tax included in the Senate bill because they said it would hit too many union-sponsored health plans and hurt middle-class workers.

And then there are an array of outstanding issues on which no consensus has been reached, like the emotionally charged issue of insurance coverage for abortions.

The House bill was passed, 220 to 215, in November. The restrictions on abortion coverage were approved, 240 to 194, with support from 64 Democrats, including 41 who also voted for passage of the bill.

The House Republican whip, Representative Eric Cantor of Virginia, said he had identified 11 “pro-life House Democrats” whose votes “could be in play” if the abortion restrictions were weakened.

There are other disagreements.

Members of the Congressional Hispanic Caucus, for example, strongly oppose a provision in the Senate bill that would bar illegal immigrants from buying health insurance through new government-regulated exchanges, or marketplaces, even if they could afford to pay the full cost with their own money. The House bill would permit illegal immigrants to buy coverage on their own.

Congressional aides and lobbyists pointed out several other obstacles to persuading House Democrats to approve the Senate bill.

If the Massachusetts race is seen as a referendum on the health care issue, many rank-and-file Democrats could be wary of defying public sentiment. And while many Democrats have recently expressed a desire to finish the health care legislation and move on, the prospect of needing future changes to the Senate bill would potentially drag out the health care issue for many more months.

In addition, if Democrats use a budget bill as the vehicle for fixing health care legislation, Republicans could challenge health policy provisions on the ground that they had no impact on federal spending or revenues. Eric M. Ueland, a lobbyist who used to work for the Senate Republican leadership, described the uncertainty surrounding a two-bill strategy this way: “It’s tantamount to the Senate saying to the House, ‘We cannot tell you what, when, why or how, but trust us, it will all work out.’ ”

Ms. Pelosi, however, said that it was Republicans who could not be trusted on the health care issue, and that Democrats would not squander the opportunity to pass a bill.

“I heard the candidate in Massachusetts, the Republican candidate, say ‘Let’s go back to the drawing board,’ ” Ms. Pelosi said. “The drawing board for the Republican Party on health care is to tear it up and throw it away and shred it and never revisit it.”

She added: “Back to the drawing board means a great big zero for the American people.”