House Speaker Nancy Pelosi (D., Calif.) battled to gather the 218 votes she needs to ensure passage. Asked if she has the necessary votes, Ms. Pelosi told reporters, “We will.”

Democrats hailed the backing of the AMA, the nation’s largest doctors’ group, as especially significant, since its position had been in doubt. But the group’s statement of support was lukewarm, saying the measure is “not the perfect bill.” AARP, the largest senior citizens’ organization, officially endorsed the bill, citing the fact that it would help lower drug costs for seniors and make it easier for older Americans who don’t yet qualify for Medicare to buy insurance policies.

Mr. Obama made a surprise appearance in the White House briefing room, seizing on the endorsements in an attempt to provide a final burst of momentum.

“They would not be supporting it if they really believed that it would lead to government bureaucrats making decisions that are best left to doctors,” he said of the AMA. “They would not be with us if they believed that reform would in any way damage the critical and sacred doctor-patient relationship.”

Hoping for a victory on his highest domestic priority, the president plans to visit the Capitol Friday for a last-minute meeting with House Democrats. If the House approves the legislation, it would mark the first time either chamber of Congress passed a bill aimed at providing near-universal health coverage.

Republicans held a rally on the Capitol steps to denounce the bill’s estimated 10-year cost of $1.055 trillion. “This is an attack on America and our freedom,” said Rep. Joe Pitts (R., Pa.). Protesters responded with chants of “Kill the bill.”

Among Democratic leaders’ biggest remaining challenges is satisfying anti-abortion Democrats concerned that the legislation would allow federal funding of abortion. They fear a government-run health-insurance plan — commonly referred to as the public option — would include abortion coverage, and that people who receive government subsidies could use the money to buy insurance that covers abortions.

Rep. Brad Ellsworth (D., Ind.), who opposes abortion, has drafted a potential compromise. The provision would establish strict rules for insurance companies to separate public funds from individuals’ premiums, so public money couldn’t be used to fund abortions. And it would require that the public option be administered by a private contractor, whose responsibilities would include segregating and managing any money that went for abortions.

The Ellsworth proposal is opposed by Rep. Bart Stupak of Michigan, a leader of the anti-abortion Democrats, who wants stronger language. But Democratic leaders are hopeful it can satisfy at least some of the roughly 40 Democrats concerned about the abortion issue.

Ms. Pelosi praised Mr. Ellsworth. “He and others who have strong pro-life positions want to see a strong health-care bill passed, and they are working very hard to find language that achieves what honors their values and the commitment not to have federal funds used for abortion,” Ms. Pelosi said. The White House undertook a full-court press Thursday. Mr. Obama met with members of the Congressional Hispanic Caucus, who are concerned by efforts to prevent illegal immigrants from purchasing health coverage through the insurance exchange included in the Democrats’ plan.

Kathleen Sebelius, the secretary of health and human services, has been on Capitol Hill for much of the week and will be meeting with wavering Democrats Friday. Nancy-Ann DeParle, director of health-care policy at the White House, will also be meeting House members Friday.

While the AMA announcement provided a boost, it carried qualifications. J. James Rohack, the group’s president, said Congress can’t fix the health-care system without also passing a bill that halts a large cut in doctors’ Medicare payments scheduled for next year.

Democrats have put a high priority on getting the backing of big-name lobbies. But several major groups have opposed the House bill or remained silent on it. Insurers, for example, strongly oppose the bill because they say the new government health-insurance program would drive them out of business.

Despite the AMA’s support, doctors remain fragmented over the bill. Several specialist groups as well as state medical associations say they can’t support the public insurance plan because they believe it would drive down government payment rates.

—Jonathan Weisman contributed to this article.