WASHINGTON — President Obama, making his final push for a health care overhaul, called Wednesday for Congress to set aside political gamesmanship and allow an “up-or-down-vote” on the measure, so that Democrats can pass the legislation and he can sign it into law, after nearly a year of debate.

“I believe the United States Congress owes the American people a final vote on health care reform,” Mr. Obama said in a brief 15-minute speech in the East Room of the White House. He called on Democratic leaders of both chambers to schedule a vote in the next few weeks, adding, “From now until then, I will do everything in my power to make the case for reform.”

Moments after Mr. Obama spoke, the White House announced that he would travel to Pennsylvania and Missouri next week to talk about the health legislation.

Wednesday’s remarks, made to a group of sympathetic medical professionals, many of them clad in traditional white lab coats, marked Mr. Obama’s entry into the end game of Washington’s long and divisive health care debate. With Republicans unified in opposition to the measure, Mr. Obama used his appearance to make the case to the public that while he is willing to accept Republican ideas, starting over, as Republicans are demanding, does not make sense.

He called on Democrats to stick with him.

“This has been a long and wrenching debate,” Mr. Obama said, adding that while health care “easily lends itself to demagoguery and political gamesmanship,” that is no reason “for those of us who were sent here to lead to just walk away.”

In the short 15-minute speech, the president avoided using the word “reconciliation,” the name for the parliamentary tactic that Democrats must now use to avoid a Republican filibuster of the bill. But senior advisers to the president made clear that is his plan.

“This has been laid out in a way that provides us the maximum flexibility to get it done,” Robert Gibbs, the White House press secretary, told a small group of reporters who gathered in his office before Mr. Obama spoke. But reconciliation could prove a heavy lift on Capitol Hill. At a bipartisan health forum at Blair House last week, Mr. Obama laid out an 11-page synopsis of his plan, without providing the House and Senate Democratic leadership with legislative language. It will now be up to Nancy Pelosi, the speaker of the House, and Harry Reid, the Senate majority leader, to produce that language, and then send it to the Congressional Budget Office for an analysis of how much the measure will cost. Getting that done in several weeks, as Mr. Obama says he expects, could prove difficult.

Friday will mark one year since Mr. Obama kicked off his plans for a major health care overhaul, with a high-profile forum at the White House that included lawmakers, insurance industry and hospital executives, medical professionals, representatives of the pharmaceutical industry and others with a stake in the debate.

On Wednesday, after 12 months of legislative hearings, town hall meetings, speeches, polls and debates, Mr. Obama made clear that he expects Democrats to line up behind the plan, no matter how skittish they feel about their re-election prospects in the fall.

“The American people want to know if it’s still possible for Washington to look out for their interests and their future,” Mr. Obama said. “They are waiting for us to act. They are waiting for us to lead. And as long as I hold this office, I intend to provide that leadership. I don’t know how this plays politically, but I know it’s right. And so I ask Congress to finish its work, and I look forward to signing this reform into law.”

Since he convened last week’s forum at Blair House, Mr. Obama has been laying the groundwork for the course he is now pursuing. He concluded the Blair House meeting by saying he was open to incorporating Republican ideas, but that Democrats would go forward on their own if he did not see any evidence of Republican cooperation.

On Tuesday, in a letter to Congressional leaders, Mr. Obama said he was open to pursuing four specific ideas raised by Republicans during the Blair House forum, including establishing “health courts” to resolve medical malpractice claims and encouraging the use by individuals of medical savings accounts that get favorable tax treatment.

But even as Mr. Obama sent the letter, his chief of staff, Rahm Emanuel, and top health policy adviser, Nancy Ann DeParle, went to Capitol Hill to meet with House Speaker Nancy Pelosi and Senate Democratic leader Harry Reid and prepare a final legislative package that they would be able to pass with simple majorities in each house. The leaders are still working on the details of that package. “We’re getting closer,” Jim Manley, Mr. Reid’s spokesman, said shortly before the president’s remarks. He did not elaborate.

With Republicans accusing Democrats and Mr. Obama of trying to ram the bill through Congress, the president and his allies are making the case that in fact, comprehensive health legislation has already passed both chambers, garnering a majority in the House and a supermajority in the Senate. Technically, they say, reconciliation will be used only to pass a small package of fixes to the original bills.

The health bill, Mr. Obama said, “deserves the same kind of up-or-down vote that was cast on welfare reform, the Children’s Health Insurance Program, Cobra health coverage for the unemployed, and both Bush tax cuts,” Mr. Obama said, citing other measures that have been adopted using reconciliation.

Under their tentative plan, the House would first approve the bill that was adopted by the Senate on Christmas Eve. Mr. Reid and Ms. Pelosi would also draft a package of changes to be approved by both chambers in a separate reconciliation bill. The reconciliation package would effectively smooth out some of the differences between the House and Senate versions.

The whole bundle would be sent to Mr. Obama to sign into law.

But while that sounds feasible, carrying out the strategy could yet prove tricky. Senate Republicans could try offering countless amendments as a delaying tactic. And Ms. Pelosi could have difficulty rounding up the necessary votes to pass the reconciliation package in the House, because it will strip out anti-abortion language that some Democrats favor.