House Republicans on Wednesday dropped a bill that would have banned abortions after 20 weeks, abandoning legislation that at one time seemed certain to pass the chamber but fell victim to intra-party disputes over concerns that the law would alienate women voters.

The failure of the bill, which was intended to be Congress' first anti-abortion legislation of the new session, reflects divides in the GOP just weeks after it assumed control of both houses for the first time in eight years.

Instead, the House will vote Thursday -- the 42nd anniversary of the Roe v. Wade decision -- on a bill that would ban the use of tax dollars for abortions, the same law that was passed by the House nearly one year ago but died in the Senate, which was then controlled by Democrats.

The substitute bill would make permanent the so-called Hyde amendment, which bans all federal money for abortion services. Currently, Congress simply renews the amendment each year, which it has done since the mid-1970s. Voting on the bill Thursday would provide Republicans with a symbolic act on the same day that the anti-abortion March for Life is scheduled to begin in Washington.

The failed bill, which reflected the idea that a fetus can feel pain at 20 weeks, would have criminalized virtually all abortions for pregnancies of 20 weeks or longer. It would offer some exceptions, including for victims of rape that have already been reported to authorities.

But some Republicans, including female members of Congress, objected to that requirement, saying that many women feel too distressed to report rapes and should not be penalized. A 2013 Justice Department report calculated that just 35 percent of rapes and sexual assaults were reported to police.

"The issue becomes, we're questioning the woman's word," Rep. Renee Ellmers, R-N.C., said earlier Wednesday. "We have to be compassionate to women when they're in a crisis situation."

There were also objections to the bill's exemption for minors who are victims of incest and have 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."

There was concern that the bill would have looked bad for the Republican Party as it struggles to court female voters in the 2016 presidential and congressional elections, and primary and general election candidates could have turned the vote around on the Republicans. The GOP also wants to demonstrate that it can focus on issues that matter to voters and not get bogged down in gridlock.

But members who backed the 20-week bill were furious that those who shied away didn't raise their objections until essentially the last minute.

“We’ve been working on this for two years. Where were they?” a source who is close to the process told Fox News on Wednesday afternoon.

The source added that it was expected that the abortion bill would be one of the new Congress's first votes of the session, and that any members suggesting otherwise are “being dishonest.”  

Thursday's debate was timed to coincide with the annual march on Washington by abortion foes marking the anniversary of the Supreme Court's Roe v. Wade decision in 1973 legalizing abortion.

In a statement, Family Research Council President Tony Perkins said he was disappointed by the failure of the 20-week measure, but said he was encouraged that Congress would vote on banning taxpayer funding of abortions.

"Americans have been forced to violate their conscience and religious convictions long enough by being made to fund President Obama's massive abortion scheme," Perkins said.

Rep. Trent Franks, R-Ariz., a chief sponsor of the 20-week bill, called it "a sincere effort" to protect women and "their unborn, pain-capable child from the atrocity of late-term abortion." He had also said GOP leaders "want to try to create as much unity as we can."

The White House had threatened to veto the legislation, calling it "an assault on a woman's right to choose."

Democrats were strongly against the legislation and said the measure was nothing more than a political gesture.

"This is not only insulting to the women of this country, but it's just another pointless exercise in political posturing," said Rep. Carolyn Maloney, D-N.Y. "It will never become law."

The GOP rift on the issue was discussed Wednesday at a private meeting of House Republicans, who by a large majority are strongly anti-abortion.

House Majority Leader Kevin McCarthy, R-Calif., said in a brief interview earlier Wednesday that he believed the House would debate the bill as planned. But he did not rule out changes.

"We're moving forward," he said earlier Wednesday. "There's a discussion and we're continuing to have discussions."

The legislation would have allowed an exception where an abortion is necessary to save the mother's life.

Under the bill, those performing the outlawed abortions could face fines or imprisonment of up to five years.

A report this week by the nonpartisan Congressional Budget Office cited estimates by the federal Centers for Disease Control and Prevention that about 10,000 abortions in the U.S. are performed annually 20 weeks or later into pregnancies. The budget office estimated that if the bill became law, three-fourths of those abortions would end up occurring before the 20th week.

The House approved a similar version of the bill in 2013, but the measure was never considered in the Senate, which was then controlled by Democrats. Its fate remains uncertain in the Senate, where anti-abortion sentiment is less strong than in the House.

Fox News' Chad Pergram and Shannon Bream and The Associated Press contributed to this report.