WASHINGTON - In an embarrassing setback, House Republicans abruptly decided Wednesday to drop planned debate of a bill criminalizing virtually all late-term abortions after objections from GOP women and other lawmakers left them short of votes.

The decision came on the eve of the annual March for Life, when thousands of anti-abortion demonstrators stream to Washington to mark the anniversary of the 1973 Supreme Court decision that legalized abortion. It also came with GOP leaders eager to show unity and an ability by the new Republican-led Congress to govern efficiently.

Despite a White House veto threat, Republican leaders had planned on Thursday House passage of the legislation, which would ban most abortions after 20 weeks of pregnancy.

But they ran into objections from women and other Republican lawmakers unhappy that the measure limited exemptions for victims of rape or incest to only those who had previously reported those incidents to authorities.

The rebellious lawmakers argued that that would put unfair pressure on women who often feel shame or fear retaliation if they report those assaults.

In a complication GOP leaders were not able to resolve, they then ran into objections from anti-abortion groups and lawmakers when they discussed eliminating the reporting requirements.

House Rules Committee Chairman Pete Sessions, R-Texas, said leaders made the decision after meeting "really, all day" with rank-and-file lawmakers.

Congressional Democrats who solidly oppose the legislation, along with abortion rights advocates, mocked the GOP's problem. Rep. Jim McGovern, D-Mass., said Republicans suffered "a meltdown."

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."

Instead of the late-term abortion bill, the House will debate legislation Thursday banning taxpayer funding for abortion - a prohibition that is already largely in effect.

Though Republicans hadn't ruled out dropping the bill, their turnabout came as a surprise.

Earlier in the evening, one leading GOP dissident said she would support the bill, suggesting that the revolt might be ebbing. In a posting on her Facebook page, Rep. Renee Ellmers, R-N.C., added, "I have and will continue to be a strong defender of the Pro-Life community."

Earlier Wednesday, Ellmers said she and other Republicans were objecting to the reporting requirement.

"The issue becomes, we're questioning the woman's word," she said in an interview. "We have to be compassionate to women when they're in a crisis situation."

A 2013 Justice Department report calculated that just 35 percent of rapes and sexual assaults were reported to police.

There were also objections to the bill's exemption for incest, which covered only minors who have already reported the incident.

"So the exception would apply to a 16-year-old but not a 19-year-old?" said Rep. Charles Dent, R-Pa. "I mean, incest is incest."

The divisiveness over the measure comes as Republicans, looking ahead to the 2016 presidential and congressional elections, hope to increase their support from women. In control of the entire Congress for the first time in eight years, Republicans also want to demonstrate they can focus on issues that matter to voters.