WASHINGTON (AP) — House Democrats are scrambling to secure enough support to pass President Barack Obama's historic health overhaul initiative, working to soothe last-minute concerns from rank-and-file Democrats ahead of a make-or-break vote.

Voting is set for Saturday on the 10-year, $1.2 trillion legislation that embraces Obama's goals of extending health coverage to tens of millions of uninsured Americans and putting tough new restrictions on insurance companies.

Obama was set to make a personal appeal to the Democratic rank and file in a visit Friday to Capitol Hill. That was called off late Thursday after the shootings at Fort Hood, Texas, and rescheduled for Saturday.

Action on health legislation was slowed as senators waited for the Congressional Budget Office to weigh in on a bill written by Majority Leader Harry Reid in consultation with the White House and key committee chairmen. Senate votes could slip until next year, but in the House Democratic leaders pressed forward.

They expressed optimism that when it came time to vote, they'd have the majority needed to prevail in the 435-seat House.

Asked Thursday if she had the votes, Speaker Nancy Pelosi replied: "We will."

Pelosi and other Democratic leaders were finalizing language to bar federal funding of abortion and resolving a flare-up over the treatment of illegal immigrants in the legislation that had Hispanic lawmakers up in arms.

Members of the Congressional Hispanic Caucus object to a provision in the Senate legislation — backed by the White House — that bars illegal immigrants from buying health insurance within a proposed new marketplace, or exchange, even if they use their own money to buy from private companies.

Illegal immigrants can buy private health insurance now, so some lawmakers say the White House position goes too far. The House bill doesn't have that language, and several members of the Congressional Hispanic Caucus met with Obama at the White House on Thursday to tell him that if that changed, he could lose as many as 20 votes.

"I think that he got our message," Rep. Nydia Velazquez, D-N.Y., head of the Hispanic Caucus, said afterward.

House leaders said that, in keeping with the Hispanic Caucus' demands, there was not likely to be any prohibition added to the House bill against illegal immigrants shopping in the exchange.

Democrats were trying to toughen prohibitions in the bill against federal funding for abortions in a way that would satisfy enough anti-abortion Democrats. The U.S. Conference of Catholic Bishops was involved in the talks and a resolution appeared within reach late Thursday.

The House effort picked up two major endorsements Thursday, from the powerful seniors' lobby AARP and the American Medical Association.

The 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.

Associated Press writers David Espo and Ricardo Alonso-Zaldivar contributed to this report.