WASHINGTON — A White House-backed overhaul of the nation's health care system weathered repeated challenges from Republican critics over taxes, abortion and more on Wednesday, and the bill's architect claimed enough votes to push it through the Senate Finance Committee as early as week's end.

"We're coming to closure," said Sen. Max Baucus, D-Mont., the committee chairman, as President Barack Obama lobbied at least one wavering Democrat by phone to swing behind the measure.

Baucus said, "It's clear to me we're going to get it passed," although he sidestepped a question about possible Republican support. Olympia Snowe of Maine is the only GOP senator whose vote is in doubt, and she has yet to tip her hand. While she has voted with Democrats on some key tests — to allow the government to dictate the types of coverage that must be included in insurance policies, for example — she has also sided with fellow Republicans on other contentious issues.

In a reflection of the intensity on both sides of the Capitol, Democratic Rep. Alan Grayson of Florida was unrepentant after claiming the Republican plan for health care was for Americans to "die quickly." Refusing to apologize, he said, "People like elected officials with guts who say what they mean. ... I stand by what I said."

That controversy aside, House Democratic leaders struggled to reduce their legislation to the $900 billion, 10-year cost that Obama has specified. Officials said numerous alternatives were under review to reduce subsidies that are designed to defray the cost of insurance for millions.

Passage in the Finance Committee would clear the way for debate on the Senate floor in mid-October on the bill, designed to accomplish Obama's aims of expanding access to insurance as well as slowing the rate of growth in health care spending overall. The bill includes numerous consumer protections, such as limits on copays and deductibles, and relies on federal subsidies to help lower-income families purchase coverage. Its cost is estimated at $900 billion over a decade.

While the legislation would not allow the government to sell insurance in competition with private companies, as Obama and numerous Democrats would like, the White House was working to make sure that some version cleared committee. Sen. Jay Rockefeller of West Virginia, a Democrat who has been outspoken in his criticism of features of the bill, said Obama called him to seek support. "I was noncommittal," the senator said.

The committee met as Senate Majority Leader Harry Reid of Nevada announced the full Senate would begin debate on health care legislation the week of Oct. 12. Initial action is expected to be slow, consumed largely with parliamentary maneuvers in which Democrats try to set the stage for passage and Republicans erect a 60-vote hurdle as a test vote.

The precise details of the bill brought to the Senate floor will be determined by Reid, in consultation from the White House and Democratic leaders of the Finance Committee and the Health, Education, Labor and Pensions Committee.

Democrats on the Finance Committee worked behind the scenes on possible last-minute changes to make insurance more affordable and accessible for lower-income families and individuals who now lack it.

Sen. Maria Cantwell, D-Wash., worked on a proposal modeled after a system in her home state that supporters say has realized significant savings. Federal subsidies ticketed for lower-income uninsured would flow to the states, which would negotiate with private insurers to provide coverage for the target population.

Aides said the proposal would be designed to provide coverage for about three-quarters of the nation's uninsured.

Inside the committee, Sen. Bill Nelson, D-Fla., won approval of a change to shield seniors from the impact of a tax increase in the bill for individuals and families seeking to exclude certain medical expenses from their income. Under current law, taxpayers who itemize their deductions are permitted to escape taxes on health costs that exceed 7.5 percent of their adjusted gross income.

Baucus' legislation would raise the threshold to 10 percent, but on a vote of 14-9, Nelson succeeded in returning it to 7.5 percent for taxpayers age 65 and over.

Moments later, Sen. Jon Kyl of Arizona sought to give younger taxpayers the same break, but his proposal failed, also on a vote of 14-9.

It was one in a string of futile Republican attempts to reshape the legislation by inserting stronger anti-abortion provisions and require photo identification to prove eligibility for benefits under federal health programs for the poor. Attempts to kill fees on health industry providers also failed, along party lines, after Baucus said the result would be to wipe out a key source of funds for the expansion of insurance.

Sen. Orrin Hatch, R-Utah, argued that provisions already in the bill to restrict federal funding for abortions needed to be tightened to guarantee they would be ironclad. He said his goal was to incorporate the restrictions into law, "so we don't have to go through it every year."

In recent years, Congress has prohibited federal funding for most abortions through annual spending bills, and Hatch's proposal would have eliminated the need for those yearly votes.

But abortion rights supporters said the proposal would have expanded the current restrictions, and could deny coverage for abortions to working women signing up for coverage through private plans.

Its approval would be a "poison pill ... if it is hung on this legislation," said Sen. Maria Cantwell, D-Wash.

The committee also rejected a proposal from Hatch to strengthen existing legal protections for health care professionals who refuse to perform abortions or other procedures on grounds of moral or religious objections.

Both failed on nearly party line votes of 13-10, with Snowe siding with most Democrats in opposition, and Kent Conrad, D-N.D., voting with Hatch.

Republicans also failed in attempts to require applicants for federal health programs to furnish photo identification as proof of eligibility, an issue that dealt with illegal immigrants. Sen. Charles Grassley, R-Iowa, said the goal was to prevent fraud, but Bob Menendez, D-N.J., objected that the proposals went beyond a required birth certificate required as proof of citizenship.

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