WASHINGTON — President Barack Obama and House Democrats scrambled on Thursday to secure the votes to pass a historic health care overhaul initiative, working to ease disagreements with rank-and-file over abortion and illegal immigrations.

Obama met at the White House with several Hispanic lawmakers who oppose any prohibition on the ability of illegal immigrants to use their own money to purchase health coverage in a new government-run marketplace.

“He listened to us. We listened to him,” said Rep. Nydia Velazquez, D-N.Y., head of the Congressional Hispanic Caucus. “We made it very clear that 20 votes in the Hispanic caucus” depend on the language in the House bill. Currently, there is no prohibition in the legislation, but the White House backs such a ban and one exists in the Senate bill.

“I think that he got our message,” Velazquez said.

House Rules Committee Chairwoman Louise Slaughter, D-N.Y., said later that she did not believe there would be any change to the House bill.

The second-ranking Democrat in the House said lawmakers would debate and vote Saturday on the $1.2-trillion, 10-year measure that expands coverage to millions of uninsured. In a major boost, the American Medical Association and the powerful seniors’ lobby AARP both threw their weight behind the bill. AARP, with its 40 million members, promised to run ads and contact activists to gin up support.

Obama planned a rare visit to the House Friday morning to persuade wavering Democrats.

Democratic opponents of abortion — under pressure from Catholic bishops — want stronger provisions written in the bill that no federal funds would be used to finance abortion in coverage bought in the government-run exchange.

Language being circulated by one anti-abortion Democrat, Rep. Brad Ellsworth of Indiana, seemed likely to be the basis for an agreement. Ellsworth’s language aims to strengthen stipulations already in the bill against federal money being used to pay for abortions. It would still allow people to pay for abortion coverage with their own money.

Slaughter said she expected that language to be included in the bill.

Obama heralded the support of the two groups — AARP and the AMA.

“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, D-Calif. “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 and other Democratic leaders were working to nail down the majority votes they’ll need to pass the bill.

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.

Pelosi, Majority Leader Steny Hoyer and other House leaders spent Thursday in back-to-back meetings on final details of the bill. Hoyer, D-Md., 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.”

If Democrats were coalescing, so were their opponents. Thousands of conservatives rallied outside the Capitol on Thursday, chanting “Kill the bill!”

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.