WASHINGTON — President Barack Obama is traveling to Capitol Hill on today to try to close the sale on his signature health care overhaul, facing a make-or-break vote in the House certain to be seen as a test of his presidency.

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Obama scheduled a late-morning visit with House Democrats convening a rare Saturday session on legislation to remake the U.S. health care system, extending coverage to tens of millions now uninsured and banning insurance company practices such as denial of coverage based on pre-existing medical problems.

Late Friday, House Democrats cleared an abortion-related impasse blocking a vote and officials expressed optimism they had finally lined up the support needed to pass Obama’s signature issue.

Under the arrangement, Democratic Reps. Bart Stupak of Michigan, Brad Ellsworth of Indiana and other abortion opponents were promised an opportunity to insert tougher restrictions into the legislation during debate on the House floor.

The leadership’s hope is that no matter how that vote turns out, Democrats on both sides of the abortion divide will then unite to give the health care bill a majority over unanimous Republican opposition.

“We wish to maintain current law, which says no public funding for abortion,” Stupak said. “We are not writing a new federal abortion policy.”

Ellsworth added, “From day one, my goal has been to ensure federal tax dollars are not used to pay for abortions and to provide Americans with pro-life options on the exchange. And I am proud to be part of an effort to help make this goal a reality.”

With Democrats’ command of the necessary votes looking tenuous in the final hours, Obama threw the weight of his administration behind the effort to round up support. He and top administration officials worked the phones to pressure wavering lawmakers.

Rep. Jason Altmire, D-Pa., said he heard Friday from Obama, White House Chief of Staff Rahm Emanuel, Health and Human Services Secretary Kathleen Sebelius and Education Secretary Arne Duncan.

Their message: “This is a historic moment. You don’t want to end up with nothing,” said Altmire, who remained undecided.

Democratic leaders hoped to hold the vote Saturday evening, but Majority Leader Steny Hoyer said it could slip.

Democrats hold 258 seats in the House and can afford 40 defections and still wind up with 218, a majority if all lawmakers vote. But all 177 Republicans were expected to vote “no,” and Democratic leaders faced a series of complications trying to seal the needed votes for their complex and controversial legislation that would affect one-sixth of the economy and touch the lives of countless Americans.

In the GOP’s weekly radio address, Mississippi Gov. Haley Barbour said Democrats should scrap their ambitious legislation and concentrate on modest health care changes that could find bipartisan support.

“The House Democrats’ health care bill should be withdrawn and reworked,” he said.

Tuesday’s elections — in which Democrats lost two governors’ races — sent a message that voters care about jobs, not growing the size of government, Barbour said.

The final hurdle for the Democrats was a controversy over federal funding for abortion, which simmered into Friday night with tensions running high as party leaders shuttled between meetings of anti-abortion and abortion rights lawmakers.

Federal law currently prohibits the use of federal funds to pay for abortions except in the case of rape, incest of situations in which the life of the mother is in danger. That left unresolved whether individuals would be permitted to use their own funds to buy insurance coverage for the procedure in the federally backed insurance exchange envisioned under the legislation.

Democrats have little room for error, with the prospect of the 2010 midterms looming large and a some of their own moderates already declaring their opposition.

The 10-year, $1.2 trillion House bill would create a new federally supervised insurance marketplace where the uninsured could purchase coverage.

Consumers would have the option of picking a government-run plan, the most hotly contested item in the legislation.