After spending the last few years butting heads with his most conservative members, House Speaker John A. Boehner has a new headache: a revolt by moderates.

Tired of staying quiet while tea-party-minded conservatives pull the Republican majority further to the right, more temperate voices are starting to rise in the new GOP-led Congress.

Female lawmakers pushed the party to drop Thursday’s planned vote on legislation that would ban abortions after 20 weeks of pregnancy, forcing leaders to abruptly switch course and pass a different antiabortion bill.

Last week, a surprisingly large group of 26 House Republicans refused to support an amendment that called for ending deportation deferrals of young immigrants brought to the U.S. illegally as children. Those dissenters came within one vote of tanking the measure aimed at so-called Dreamers.

Most of these Republicans bristle at being called moderates, preferring to be seen as pragmatists worried that the party’s hard-line policies will backfire with voters, particularly in the 2016 presidential race. Many hail from moderate electoral districts in California, New York and Illinois, where conservative positions on immigration, abortion and gay rights are unpopular.

These lawmakers warn that Republican message votes, which may appeal to party stalwarts but have little chance of overcoming Democratic filibusters or presidential vetoes, will only serve to complicate their own re-elections and leave the GOP with little to show for its new majority.

The shifting terrain represents an unexpected — but not wholly unwelcome — new challenge for Boehner as he struggles to control his party.

Rather than trying to appease conservatives by pursuing bills that have little hope of becoming law, GOP leaders, who have had their own battles with the party’s right flank, suddenly find themselves with a faction of vocal Republican lawmakers who say they are interested in scoring legislative victories rather than political points.

The female lawmakers and others worried that the bill’s exemption for “reportable” rapes evoked the widely condemned comment by former Republican Rep. Todd Akin that pregnancies rarely result from “legitimate rape.”

The bill made exceptions to the 20-week ban in cases of incest, when the life of the mother was endangered or after “reportable” rapes, effectively requiring women to report the sexual assaults to police before they could obtain an abortion.

“Social issues like abortion are important to young voters, because I think recent statistics will show they are the people receiving the most abortions,” said Emily Dean, a sophomore occupational therapy major.

Dean said people want a say in their lives and their future child’s life.

“Abortion will be an important issue in the next presidential election because of recent bills in congress such as one wanting to stop federally funded abortions on the president’s health care plans,” said Dean.

Renee Duvall said she would have supported the bill.

“Although I do not support abortion personally I do believe women should have access to medical and safe abortions. However, I believe the abortion should occur before the age of viability,” said Duvall, a junior politcal science major.