WASHINGTON — A final agreement nearly in hand, President Barack Obama and Democratic leaders are about to embark on one last sales job that will determine the outcome of the president’s signature health care overhaul.

It will come down to a phenomenal effort by congressional leaders and the White House to win over skittish lawmakers after a year of incendiary debate, even as Obama keeps up campaign-style appearances designed to fire up public support.

A closed-door meeting in House Speaker Nancy Pelosi’s office Wednesday evening moved congressional leaders and administration officials close to agreement on such issues as additional subsidies to help lower-income families purchase health insurance and more aid for states under the Medicaid program for low-income Americans.

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Democrats still need to see a final cost estimate from the Congressional Budget Office — and want to ensure it stays around $950 billion over 10 years — but they made plans to begin to read the bill to rank-and-file Democrats at a caucus meeting Thursday.

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“We’re going to get started,” Pelosi, D-Calif., said after her meeting with White House Chief of Staff Rahm Emanuel, Senate Majority Leader Harry Reid, D-Nev., and other key officials. Some unanswered questions remain, Pelosi said, “but we’re hoping that we’ll get those answered over the course of the reading. It’s not much.”

“I’m very pleased about where we are,” she said.

Obama invited members of the Congressional Black Caucus and the Congressional Hispanic Caucus to meet with him Thursday at the White House to discuss the health legislation. The White House also said Obama would travel to northeastern Ohio on Monday for an appearance near the hometown of an uninsured cancer patient named Natoma Canfield, whom the president has made a symbol of the need for reform.

It will be Obama’s third event on health care in a week. In St. Charles, Mo., on Wednesday Obama shouted to a crowd: “The time for talk is over. It’s time to vote.”

At stake is the fate of Obama’s call to expand health care to some 30 million people who lack insurance and to prohibit insurance company practices such as denial of coverage on the basis of pre-existing medical conditions. Almost every American would be affected by the legislation, which would change the ways people receive and pay for health care, from the most routine checkup to the most expensive, lifesaving treatment.

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House and Senate Democrats are working on a complex rescue mission for the health care legislation, which appeared on the cusp of passage late last year before Senate Republicans gained the strength to sustain a filibuster that could prevent final passage. The White House is pushing for a vote by the House before Obama leaves on a foreign trip at the end of next week.

The current plan is for the House to approve the Senate-passed bill from late last year, despite serious objections to numerous provisions. Both houses then would pass a second bill immediately, making changes in the first measure before both could take effect. The second bill would be debated under rules that bar a filibuster, meaning it could clear by majority vote in the Senate without Democrats needing the 60-vote supermajority now beyond their reach.

Republicans have vowed to do everything they can to thwart the plan, and for the Democrats, some policy questions remain unsettled.

Obama already has moved to eliminate a couple of special deals in the Senate bill that turned off voters when they became public, including extra Medicaid funding for Nebraska — derided by critics as the “Cornhusker kickback.” Late Wednesday the White House said the president was pushing to strip out a number of deals that remain, possibly including a provision sought by Sen. Max Baucus, D-Mont., providing Medicare coverage for residents of Libby, Mont., who suffer from asbestos-related illnesses because of a now-closed mining operation.

Pelosi and other House Democrats want to include Obama’s proposed overhaul of the nation’s student loan programs in the second, fix-it health care bill. The measure would require the Education Department to originate all student assistance loans, effectively eliminating a role for banks and other private lenders. That idea has run into opposition from several Senate Democrats.

Another issue was a demand from a dozen states for additional funds under Medicaid. And a dispute over federal funding for abortion threatens to peel off votes from some anti-abortion Democrats in the House, but perhaps not enough to sink the bill if it isn’t resolved.

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