Washington (CNN) Mark it down as a rare win for House GOP moderates. After scrambling into the evening on Wednesday, House Republican leaders decided to scrap a vote on a controversial anti-abortion measure scheduled to coincide with an annual gathering of anti-abortion advocates on Thursday because they couldn't round up enough support.

Two senior House GOP aides tell CNN that after discussions with members on Wednesday night they are no longer voting on the late-term abortion bill and are now voting instead on a bill banning taxpayer money for abortions.

"Some concerns were raised by men and women members that still need to be worked out," one of the aides told CNN. "Tomorrow we will vote to advance the pro-life cause and remain committed to continue working through the process on pain capable to make sure it too is successful."

A similar measure that calls for banning taxpayer money for abortions passed the GOP-controlled House last year.

Rep. Pete Sessions, chairman of the Rules Committee which met on Wednesday night to address the matter, said the decision to change plans came after discussions with members throughout the day.

"It's my hope that this resolution will address the concerns of our members and will allow us to move forward to where we are able to consider this important legislation - to discuss it on the floor and to move it forward," he said.

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Democratic Rep. Jim McGovern said the "bill led to a meltdown" in the Republican conference and criticized the decision to take up the alternate measure that had previously passed.

"Maybe we can Xerox your testimony from last year," McGovern said dryly, adding, "We've done this before."

The rebellion was initially headed up by a group of female House Republicans that pointed out the vote could threaten the party's efforts to reach out to women and young people.

The "Pain Capable Unborn Child Protection Act," is a bill banning so called "late-term abortions" -- those involving procedures for women who are beyond 20 weeks into their pregnancy. Several House GOP women protested language in the bill that requires those women who seek an exception to the ban because they were raped have to back up their claim with a police report. A similar measure has passed the House in 2013, but this time some female members -- including some who voted for it last time -- are pushing for that requirement to be stripped out.

Discussion about the issue at a closed door meeting on Wednesday morning got so tense that congressional aides were kicked out of the meeting when the debate turned emotional, according to several GOP sources.

The internal feud placed leaders in an awkward spot, because they targeted the vote for Thursday, the same day as the March for Life in Washington and the 42nd anniversary of the landmark Supreme Court decision, Roe v. Wade, which negated state laws that prevented a woman from having an abortion based on the constitutional right to privacy.

On Tuesday, two female Republicans -- Rep. Renee Ellmers of North Carolina and Rep. Jackie Walorski of Indiana -- removed themselves as cosponsors of the legislation. Walorski later posted on her Facebook page that she would vote for the bill, but she declined to comment on the issue further.

Out of the 246 Republicans in the House, 22 are women.

CNN reached out to several female House GOP members, who were seen huddling on the House floor during votes on Wednesday, but most declined to talk about their talks with leaders.

Missouri Rep. Vicky Hartzler supports the bill. When asked about the discussions about the rape provisions she told CNN, "We're just figuring out the best way to get it passed in the long run. We will figure that out."

Arizona GOP Rep. Trent Franks, the primary author of the bill, had predicted the bill could pass if the language regarding rape stays in the bill. He maintained that public opinion polls demonstrate Americans of all ages back his legislation.

"Everything that I know about millennial voters, the younger voters, is that they are more pro-life than us old guys," Franks said.