WASHINGTON — With their party’s candidate struggling in Massachusetts in a race for what should be the safest of Senate seats, Congressional Democrats are growing increasingly unnerved about the political consequences of the health care overhaul even as their leadership closes in on a final agreement.

Many Democrats say they still believe the best course is to forge ahead and enact sweeping health care changes, allowing them to claim the party has conquered a domestic issue that has long defied a legislative resolution.

But they also say the health fight has dragged on for far too long, denying Democrats the opportunity to concentrate on issues that are foremost in the minds of many Americans, jobs and the health of the economy.

Now the prospect of Attorney General Martha Coakley of Massachusetts losing on Tuesday in the special election to fill the seat of the late Edward M. Kennedy — the longtime champion of a health care overhaul — is intensifying anxiety among Democrats who were already worried about the 2010 midterm election environment.

Democrats warn of panic in the ranks should the Republican candidate, Scott Brown, prevail. Highlighting the sense that the political climate is shifting rapidly, the White House announced Friday that President Obama would travel to Massachusetts on Sunday to campaign for Ms. Coakley, hoping to generate Democratic enthusiasm in a contest that will hinge on turnout. The decision to put the president’s political prestige on the line after the White House initially said he would not make a trip was a gauge of how seriously the administration was taking the threat.

A victory by Mr. Brown could cause the fragile Democratic coalition behind the health legislation to unravel and put approval of the measure itself in jeopardy. Were he to win and take his seat before final consideration of the health legislation, Democrats would be one vote short of the 60 needed to get the bill through the Senate.

Senate Democrats say that in the event of a close race, getting the required election certification and seating a new senator could take up to two weeks. Democrats were considering whether to try to hold the final health care vote before Mr. Brown took his seat if he won, so they could use their 60-vote majority for one final victory — a move sure to inflame Republicans and pose political risks for Mr. Obama and his party.

But top Democratic officials said it was unlikely they would try to jam the measure through if the Massachusetts election went against them. Other options would be to try to persuade the House to pass the Senate version and avoid another Senate vote or to employ a procedural shortcut that would negate the need for 60 votes but limit the scope of health changes Congress could consider.

Democratic strategists also warned that a Republican victory in Massachusetts could fundamentally alter the outlook for the 2010 Congressional election season by sparking retirements among vulnerable Democrats.

For the first time, Democratic operatives said privately that control of the House could be at stake if enough Democrats saw the Massachusetts race as evidence they were headed toward defeat in November and decided to forgo a race. Another Democratic House incumbent, Representative Vic Snyder of Arkansas, announced Friday that he would retire, giving Republicans a good opportunity to pick up the seat in November.

Senior Democrats in Congress and the White House said they continued to believe Ms. Coakley would win in Massachusetts, but they acknowledged that her loss could have severe political consequences for them.

“It would not be good,” said Representative Deborah Wasserman Schultz of Florida, a vice chairwoman of the Democratic Congressional Campaign Committee.

Echoing comments by Mr. Obama on Thursday, Democratic leaders said the best political course for Democrats was to finish the job on the health bill.

“The greatest and the most important thing we can do is have success here at delivering on an intractable problem that has stymied Washington for 70 years,” said Senator Robert Menendez of New Jersey, chairman of the Democratic Senatorial Campaign Committee. “Democrats will be able to say we have gotten something done in Washington.”

Other Democrats said they remained uncertain of whether they could turn the health care measure into a political benefit ahead of the November elections, but they were sure that allowing it to collapse would be a serious misstep.

“We know that it is bad news if we don’t get it done,” said Representative James P. McGovern, Democrat of Massachusetts. “If we do get it done, it might be bad news or it might not be. So we need to get this done and start talking about something else.”

Representative Phil Hare, Democrat of Illinois, agreed: “We have to get this behind us. We have to pivot to jobs.”

Several Democrats said they were convinced that much of the public would embrace the health legislation once its benefits became known and that Democrats would be able to run proudly on their accomplishment.

“We are on the verge of completing legislation that is in a league with Social Security and Medicare,” said Representative Rosa DeLauro, Democrat of Connecticut. “It has the potential to change people’s lives.”

But some in the party warned that the Democratic Congress was on the brink of a mistake that could cost lawmakers dearly.

Representative Gene Taylor, a conservative Mississippi Democrat and opponent of the health plan, said its nearly $1 trillion cost and the lack of widespread public enthusiasm for it adds up to a political miscalculation.

“Why in the heck are we spending that amount of money for something the American people don’t want?” asked Mr. Taylor, who said the Democratic situation reminded him of the climate before the Republican takeover of the House in 1994. “I was here for 1994, and I know what ugly looks like.”

Top Democrats said they believed the Massachusetts race was being wrongly interpreted as a referendum on the health care legislation when the fact that Ms. Coakley was locked in a tight race in heavily Democratic Massachusetts was due more to her running a complacent campaign and other errors.

“There will be more panic than is justified because it was more peculiar to her,” said Representative Barney Frank, a fellow Massachusetts Democrat.

Democratic supporters of the health plan said the party could not afford to back away now.

Said Representative Xavier Becerra of California, a member of the Democratic leadership, “We are on the verge of doing something that most Americans did not believe we could accomplish.”