Washington (CNN) - In a special Saturday session, the House of Representatives began debating health care legislation crafted by House Democrats, as lawmakers on both sides of the aisle considered an amendment to the bill that would put restrictions on abortion funding.

President Barack Obama made a rare visit to Capitol Hill earlier in the day to meet with members of the House Democratic caucus and push forward proposed the health care measure.

But the contentious issue of abortion is threatening to delay Saturday's scheduled vote on the nearly $1.1 trillion bill by the full House of Representatives and possibly push it back to Sunday, according to two Democratic sources.

In a late night development, anti-abortion Democrats scored a major victory by persuading Democratic leaders to allow them to offer an amendment during the debate Saturday that would ban most abortion coverage from the public option and other insurance providers in the new so-called "exchange" the legislation would create, three Democratic sources told CNN.

The prohibition would exclude cases of rape, incest or if the mother's life is in danger.

House Democratic leadership sources said that win or lose, they hope giving abortion foes the opportunity to vote will clear the way for passage of their health care bill. But sharp differences among Democrats on the abortion issue and others, such as immigration, are raising questions over whether Speaker Nancy Pelosi currently has the 218-vote majority needed for passage of the legislation.

Several anti-abortion Democrats will offer the amendment, including Rep. Brad Ellsworth, D-Indiana, and Rep. Bart Stupak, D-Michigan.

House Minority John Boehner told reporters after debate on the legislation had begun that the GOP leadership strongly supports that amendment.

"We believe taxpayer funding of abortion is wrong, and we will do everything we can to stop that from happening, by passing the Stupak amendment," he said.

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