WASHINGTON (AP) — With thousands of abortion foes massing blocks away for their annual protest march, Republicans pushed legislation toward House passage Thursday tightening restrictions on federal financing of abortions that the White House quickly threatened to veto. But it was not the bill an embarrassed GOP had hoped to approve.

Republican leaders had wanted to approve legislation criminalizing most abortions after 20 weeks of pregnancy, a measure that had also drawn a threatened veto. Late Wednesday, they abruptly postponed the confrontation indefinitely after concluding they were short of votes.

Instead, the House began debating legislation barring taxpayer funding of abortions — a prohibition that's already largely in place. Republicans say the bill will tighten the restrictions to make sure no funds flow to abortions under President Barack Obama's health care law. It is the same as a measure the House approved last year on a near party-line vote.

"Conscientious pro-life Americans who don't want to be complicit in the wounding of women and killing of babies are paying for abortions, and many of them don't even know it," said Rep. Christopher Smith, R-N.J., a longtime abortion opponent.

Democrats mocked the GOP's failure to rally support behind the measure barring late-term abortions but said sarcastically that Republicans seemed to have unlimited numbers of bills curbing the procedure.

"Can't pass this one? Grab another. Can't pass that one? Grab the next one," said Rep. Louise Slaughter, D-N.Y. "Their insistence on attacking women's health seemingly knows no bounds."

The bill would permanently ban the use of federal money for abortions — a prohibition that's already in effect but that Congress must renew each year.

It would also go further. It would bar individuals and many employers from collecting tax credits for insurance plans covering abortion that they pay for privately and purchase through exchanges established under the health care law. It would also block the District of Columbia from using its money to cover abortions for lower-income women.

In its veto message, the White House said, "The administration strongly opposes legislation that unnecessarily restricts women's reproductive freedom and consumers' private insurance options."

The action came the day of the annual March for Life protesting the Supreme Court's 1973 Roe v. Wade decision legalizing abortion. It also came with GOP leaders eager to showcase the ability by the new Republican-led Congress to govern efficiently and avoid gridlock.

The bill that was postponed would have allowed exemptions to the late-term abortion ban for victims of rape or incest and in cases when a woman's life was in danger. But GOP leaders ran into problems because some GOP women and other lawmakers objected that the rape and incest exemptions only covered women who had already reported the crimes to authorities.

The rebellious Republicans argued that that requirement put unfair pressure on women who have already suffered. A 2013 Justice Department report calculated that only 35 percent of rapes and sexual assaults were reported to police.

Political pressures cut both ways. Leaders had resisted the awkwardness of postponing a high-profile abortion vote scheduled for the day of the anti-abortion march. And they didn't want to push anti-abortion legislation through the House that was opposed by GOP women, especially as the party tries appealing to more female voters ahead of the 2016 elections.

Yet when the leaders considered eliminating the requirement that rapes and incest be previously reported, they encountered objections from anti-abortion groups, Republican aides said. They chose not to anger that powerful GOP constituency.

The bill had virtually no chance of becoming law, thanks to opposition from President Barack Obama and an uncertain fate in the Senate, where anti-abortion sentiment is less pronounced. Even so, Republicans consider the bill an important statement of their priorities and a show of support for a vital issue for conservatives.

Supporters named their measure the Pain-Capable Unborn Child Protection Act. But Democrats touted arguments by doctors' groups like the American Congress of Obstetricians and Gynecologists, which have cited research indicating that fetuses are unlikely to feel pain until the third trimester, which starts around the 28th week.

A report Tuesday by the nonpartisan Congressional Budget Office, citing the federal Centers for Disease Control and Prevention, estimated that about 10,000 abortions annually are performed 20 weeks or later into pregnancies. The budget office estimated that if the bill became law, three-fourths of those abortions would instead occur before the 20th week.

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