WASHINGTON — Support from his own party in doubt, President Barack Obama summoned more than a dozen House Democrats to the White House Thursday, pleading with them to put aside their qualms, seize a historic moment and vote for his massive health care overhaul.

It’s the opportunity of a generation, he told them — and a chance to revive the party’s agenda after his rough first year in office.

In back-to-back meetings in the Oval Office and Roosevelt Room, Obama urged uneasy rank-and-file moderates and progressives to focus on the positives rather than their deep disappointment with parts of the bill. The lawmakers said Obama assured them the legislation was merely the first step, and he promised to work with them in the future to improve its provisions.

“The president very pointedly talked about how important this is historically,” said Rep. Raul Grijalva, D-Ariz., “how he needs our help.” Obama told them that “’this is an opportunity, it’ll give us momentum”’ on other issues, the congressman said.

Cranking up the pressure, congressional leaders said they were hoping for votes on the legislation in as soon as two or three weeks.

White House spokesman Robert Gibbs told reporters he believes the House is on schedule to approve the landmark legislation by March 18, when the president leaves for an Asian trip, and he can sign it into law “shortly thereafter.”

Concerned about fellow Democrats’ trepidation about a legislative drive that has garnered only modest public support, House leaders expressed optimism but hardly certainty that they would nail down enough support that soon. Democrats have repeatedly missed self-imposed deadlines for moving the legislation.

Obama’s revved-up personal involvement, along with the cautious tone of congressional leaders’ forecasts, illustrated the uncertainty still facing the president’s yearlong drive to push his signature legislative initiative through Congress. The outcome is important for all Americans, since the changes would affect the ways nearly everyone receives and pays for health care and failure to act would leave in place a system that many find lacking and that leaves out tens of millions of people.

Under the current strategy, Democratic leaders want Congress to send Obama the nearly $1 trillion health overhaul that the Senate passed in December, plus a separate bill making changes that House Democrats want. But there’s no decision yet on exactly what that second measure will look like.

Rep. Barbara Lee, D-Calif., among 16 lawmakers who met with the president, said Obama told them he understands the shortcomings of the current package.

“He thinks this approach is the way it’s going to get done,” said Lee, who heads the Congressional Black Caucus. 

“He said this is the first step, a foundation that we can build upon. He made a commitment to work with us on all the issues that are outstanding, and there are many,” including a desire by liberal Democrats for government-run health plans. That idea is opposed by moderate Democrats and nearly all Republicans.

Of the House Democrats Obama met with, all but two voted for a more far-reaching version of the health bill in November. The attendance list spotlighted the White House’s need to reassure those supporters on the legislation, even as it struggles to retain backing from more moderate Democrats worried about the bill’s costs and its language on abortion.

Another who attended, moderate Rep. Joe Crowley, D-N.Y., said, “I think when all is said and done we will have the votes to pass health care reform.”

House leaders were more cautious about the prospects for the measure, which is virtually sure to be opposed by all Republicans.

Rep. Steny Hoyer of Maryland, the No. 2 House Democrat, said a March 18 House vote was possible, but he added, “Until we have something concrete, it’s difficult to ask people, ‘Can you support this?”’

As if to illustrate that, Rep. Dina Titus, D-Nev., a freshman who supported an earlier version of the bill, said she is now undecided, citing questions about what the final measure would include.

“I think what’s happened in my district is there’s a great deal of uncertainty,” she said.

Rep. Nathan Deal, R-Ga., who is retiring to run for governor of his state, made the Democrats’ task a bit harder. He said he will remain in Congress to vote against the health package rather than leaving this Monday, meaning it will need 217 House votes to pass.

In a sign of movement, House Speaker Nancy Pelosi, D-Calif., and others said Democrats have already sent parts of a revised bill to the Congressional Budget Office, which will certify its price tag. The nonpartisan budget office must estimate legislation’s cost before lawmakers can vote on it.

Pelosi said she believed House Democrats would be reassured by changes to the prospective Senate bill, including an easing of a tax on high-cost health policies, higher subsidies to help low-income people purchase insurance, more generous prescription drug benefits for the elderly and the removal of federal Medicaid aid provided solely to Nebraska.

Just days after Obama made a show of bipartisanship by saying he would consider incorporating Republican ideas into the bill, a top House aide said at least two would be included: cracking down on fraudulent medical billing and exploring ways to avoid expensive malpractice trials. The aide said it was unclear whether higher federal Medicaid payments to states and GOP-proposed tax breaks aimed at discouraging unneeded medical care would be included.

Spotlighting another problem House leaders face, Rep. Bart Stupak, D-Mich., said a dozen anti-abortion Democrats will vote against the health legislation if it allows some federal funds to be used for abortions. The House bill’s abortion restrictions are tougher than the Senate’s, which Stupak said on ABC’s “Good Morning America” would let the federal government “directly subsidize abortions.”

Republicans say the legislation would create government-controlled health care that the public does not want. Sen. Lamar Alexander, R-Tenn., said Obama and House Democratic leaders are asking their members to “hold hands, jump off a cliff and hope Harry Reid catches them,” a reference to the Senate Democratic leader from Nevada.

In another event at the White House, Health and Human Services Secretary Kathleen Sebelius met with the chiefs of four major health insurance companies and asked them to provide justifications for double-digit price increases that have angered consumers. Health insurers, who have blamed rising medical costs for their own price rises, made no final commitments about what they would provide.

Obama advisers hope that highlighting the rate hikes will put pressure not just on insurers to lower rates but also on Congress to agree on a final bill.

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Associated Press reporters Ricardo Alonso-Zaldivar, Donna Cassata, Ben Evans, Ann Sanner, Liz Sidoti and Erica Werner contributed to this report.