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President Obama's sweeping vision of a health care overhaul will come to an historic debate and vote in the House this weekend.

Majority Leader Steny Hoyer, D-Md., said the House would conclude its historic debate and vote on Saturday.

"That would be my expectation," he said on the House floor, responding to a query from House Minority Whip Eric Cantor, R-Va., who asked whether lawmakers would be able to leave Washington Saturday.

"It is our intent to finish the health care bill Saturday, Saturday night or Sunday morning," he said.

Republicans will be allowed to offer their health care bill as an amendment, Hoyer said.

The Congressional Budget Office estimated that the GOP plan, while keeping premiums down and costing a mere fraction of the Democrats' bill, would cover only 3 million more Americans. By comparison, the Democrats' bill is projected to cover 36 million.

On Thursday, House Democratic leaders predicted swift passage of the bill and Obama declared health reform is closer to passage than ever before.

The bill received a huge boost Thursday from two major groups: The American Medical Association and the powerful seniors' lobby AARP. AARP, with its 40 million members, promised to run ads and contact activists to gin up support.

"I urge Congress to listen to AARP, listen to the AMA, and pass this reform for hundreds of millions of Americans who will benefit from it," Obama told reporters during an unannounced visit to the White House briefing room after the endorsements were announced.

At the other end of Pennsylvania Avenue, Democrats were listening.

"We are right on the brink," said House Speaker Nancy Pelosi. "We have an historic opportunity for us to again provide quality health care for all Americans. It is something that many of us have worked our whole political lifetimes on."

Pelosi, Hoyer and other House leaders spent Thursday in back-to-back meetings, working on the final details of the 10-year, $1.2 trillion bill, including final language on abortion and illegal immigration, and trying to nail down the 218 votes they'll need for passage. Obama planned to give them an assist Friday with a rare visit to Capitol Hill to meet with Democrats and shore up any wavering support.

Despite the optimism, work remained to be done, and a much slower timeline in the Senate made the ultimate outcome unpredictable. Action in the Senate may not come until next year, and legislation passed by the two chambers would have to be reconciled before a bill could go to Obama.

Hoyer predicted a tight vote.

"I wouldn't refer to it as a squeaker, but I think it's going to be close," Hoyer said in an interview with wire service reporters. "This is a huge undertaking."

Leaders were hoping Democratic opponents of abortion could coalesce around language strengthening restrictions already in the bill against federal funding going to pay for abortions, but anti-abortion groups weren't satisfied. On immigration, there was still a question as to whether illegal immigrants -- who would not get federal subsidies to help them buy coverage -- would be allowed to shop for private insurance within a new purchasing exchange using their own money.

The White House position is that illegal immigrants shouldn't be allowed into the exchange, but that goes too far for members of the Congressional Hispanic Caucus. Several of them met with Obama at the White House Thursday afternoon.

When it comes time to vote Pelosi will have two more Democrats to count on in the wake of Tuesday's elections. Former California Lt. Gov. John Garamendi was sworn in Thursday to a Northern California congressional seat after telling fellow lawmakers he had campaigned for health care in his race. Democrat Bill Owens is being sworn in Friday to represent a New York district long held by the GOP.

The House bill would cover 96 percent of Americans, providing government subsidies beginning in 2013 to extend coverage to millions who now lack it. Self-employed people and small businesses could buy coverage through the new exchanges, either from a private insurer or a new government plan that would compete. All the plans sold through the exchange would have to follow basic consumer protection rules.

For the first time, almost all individuals would be required to purchase insurance or pay a fine, and employers would be required to insure their employees. Insurance companies would be barred from denying coverage to people with pre-existing medical conditions or charging much higher rates to older people.

Fox News' Chad Pergram and The Associated Press contributed to this report.