Washington ? Support from his own party in doubt, President Barack Obama summoned more than a dozen House Democrats to the White House on 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.