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WASHINGTON – House Democrats are aiming to scale back the cost of their health care bill to well below President Barack Obama’s preferred price tag by giving the government a strong hand in selling insurance in competition with the private market.

Obama has sought to spend no more than $900 billion over a 10-year period. The initial cost of the House bill was more than $1 trillion. On Tuesday, House Democratic leaders received a new cost estimate of $871 billion from congressional budget umpires who measured a robust version of a so-called public option for health insurance, according to a Democratic aide.

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The figures were preliminary because no final decision on the design of the public plan had been made, said the aide, who requested anonymity in discussing the bill because the deliberations were private.

The House bill with the strong public plan would extend coverage to 96 percent of uninsured Americans and significantly reduce budget deficits.

A $871 billion bill in the House would be in line with the leading Senate bill, the $829 billion measure approved last week by the Senate Finance Committee.

House Speaker Nancy Pelosi and other liberal lawmakers have joined Obama in calling for a public insurance program as a way to drive down the costs of insurance. Republicans have opposed government-run insurance and vowed to vote against a bill establishing a public option.

Pelosi assembled Democratic lawmakers Tuesday night to try to sell them on her preferred version of the public plan, which would link payment rates to providers to Medicare rates, plus an additional 5 percent for doctors. Moderates have been concerned that those rates are too low and would hurt hospitals and other providers particularly in rural areas.

Several lawmakers said they were getting close to the 218-vote majority needed for the stronger version.

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“That’s certainly where a large majority of the caucus is,” said Rep. Chris Van Hollen, D-Md.

Leaders in both the House and the Senate were trying to finalize bills in time to begin floor debate in the next several weeks. Whether Senate Majority Leader Harry Reid, D-Nev., would include a public insurance plan in the Senate version was not clear.

In the Senate, legislation giving doctors $247 billion in increased Medicare fees over the next decade veered toward collapse, a victim of bipartisan concern over growing federal deficits.

Key lawmakers worked privately on a far less costly bill that would avert a 21 percent cut scheduled to take effect on Jan. 1 and give physicians an increase of .5 percent in 2010 and 2011.

Sen. Kent Conrad, D-N.D., said he and Sen. Charles Grassley, R-Iowa, were discussing a possible compromise that would cost $25 billion over two years and — unlike the original measure — not raise federal deficits.

The nation’s debt “doubled during the last administration and if we don’t do something, it’s going to double again in the next eight years,” Conrad said.

Anything less than the 10-year bill would mark a defeat for the American Medical Association, which has made a priority of legislation to create a new program to assure doctors reliable annual fee increases. The organization has aired television commercials in several states at a cost of $1 million or more and dispatched top officials to the Capitol in recent days to lobby lawmakers.

“Congress needs to fix this problem once and for all,” AMA President Dr. J. James Rohack said in a statement. “No more Band-Aids.”

The developments occurred as Senate leaders and White House aides met for the second straight day in the Capitol in hopes of agreeing on comprehensive health care legislation. Participants in the talks said no decisions had been made about key issues, including proposals for government insurance.

Obama has made an overhaul of the nation’s health care system a top priority. Speaking at a Democratic National Committee fundraiser in New York on Tuesday, he said Democrats tend to have their “intramural fights” but that the American people desperately need a good bill to pass.

“I want all the Democrats who are in the House to understand what a profound potential achievement this is and stay focused on the goal line,” Obama said. To his Republican critics, he said he welcomed a fierce debate over the final details but added that he would not stand for “folks sitting on the sidelines and rooting for failure.”

All the health overhaul bills on Capitol Hill would require, for the first time, that most Americans purchase insurance. Lower-income individuals and families would receive federal subsidies to defray the cost, and small businesses would receive government help to pick up part of the cost of covering their employees.

Legislation would also include consumer protections such as a bar on the insurance industry’s current practice of denying coverage on the basis of pre-existing medical conditions. Obama also wants any bill he signs to rein in the nation’s spiraling medical costs.