WASHINGTON — With thousands of anti-abortion protesters in town, Republicans are ready to push legislation through the House designed to please them. But it’s not the bill an embarrassed GOP was hoping for.

Republican leaders had planned House passage today of legislation criminalizing most abortions after 20 weeks of pregnancy, an act that would have defied a White House veto threat. But late Wednesday they abruptly postponed that confrontation indefinitely after concluding they were short of votes.

Instead, the House will vote on legislation barring taxpayer funding of abortions — a prohibition already largely in place. Republicans say the bill will tighten the restrictions and make sure no funds flow to abortions under President Barack Obama’s health care law.

The GOP reversal coincides with today’s annual March for Life protesting the Supreme Court’s 1973 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.

“I don’t see it as a failure. I see it as a victory in the process for getting legislation right,” said Rep. Marsha Blackburn, R-Tenn., a sponsor of the postponed bill.

Tony Perkins, president of the conservative Family Research Council, expressed disappointment that “a handful” of lawmakers had forced a delay in the late-term abortion restrictions but added, “We applaud the leadership for remaining committed to advancing pro-life legislation.”

Cecile Richards, president of Planned Parenthood Action Fund, said of the bill, “These attacks are so dangerous, extreme and unpopular that House Republicans can’t even get their membership lined up behind them.”

The delayed bill would allow 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 the requirement put unfair pressure on women who have already suffered.