Demonstrators turn out for “Ohio March for Life” to support ending abortion access in Ohio at the Statehouse in Columbus, Ohio, in October. Barbara Perenic/The Columbus Dispatch via Associated Press

WASHINGTON — House Republicans are moving toward early action on abortion with their new majority, voting on two measures Wednesday that make clear they want further restraints after the Supreme Court overruled the federal right to an abortion last year.

The new Republican-led House is voting on one resolution to condemn attacks on anti-abortion facilities, including pregnancy crisis centers, and on legislation that would impose penalties if a doctor refused to care for an infant born alive after an abortion attempt.

Neither is expected to pass the Democratic-led Senate, but Republicans say they are making good on promises to address the issue along with other legislative priorities in the first days in power.

“You don’t have freedom, true liberty, unless government protects your most fundamental right, your right to live,” said new House Judiciary Committee Chairman Jim Jordan, R-Ohio, who led debate on the measures.

Even so, the two measures are far from a bold statement on abortion, which has proved politically tricky for them since the June Supreme Court decision that overturned Roe v. Wade after almost 50 years and allowed states to enact near or total bans on abortion. While some Republicans have pushed to expand on the ruling with a national ban – or a compromise ban that would limit abortions after a certain point – many Republicans have rejected that option. And it has become clear that most Americans would oppose it.

A July AP-NORC poll showed Republicans are largely opposed to allowing abortion “for any reason” and after 15 weeks into a pregnancy. But only 16% of Republicans say abortion generally should be “illegal in all cases,” and a majority, 56%, say their state should generally allow abortion six weeks into a pregnancy. According to AP VoteCast, a national survey of the midterm electorate, 61% of all voters said they were in favor of a law guaranteeing access to legal abortion nationwide.

The national sentiment has made some Republicans wary of the party’s traditional full-throated opposition to abortion rights.

South Carolina Rep. Nancy Mace, who says she is opposed to abortion, said she believes the early push on the issue is misguided. She said she believes the majority of voters in her swing district opposed the Supreme Court’s decision to overrule Roe.

“This is probably not the way to start off the week,” Mace told MSNBC.

Emboldened by opposition to the Supreme Court decision, Democrats enthusiastically opposed the two measures, predicting that Republicans were only laying the groundwork for a national ban.

Republicans supporting the bill took pains not to connect it with overturning Roe.

“I want to be absolutely clear that this bill has nothing to do with the Supreme Court decision,” said Missouri Rep. Ann Wagner, the Republican sponsor of the bill.

Rep. Barry Loudermilk of Georgia said the measures passed Wednesday reflect what Republicans see as immediate abortion priorities. House Republicans still “need to have a discussion” about more wholesale changes, namely an abortion ban, he said.

Loudermilk said he thinks the issue should be left to the states for now, “otherwise we start muddying the waters again.”

Emboldened by public opposition to the Supreme Court decision, Democrats enthusiastically opposed the measures, predicting that Republicans were only laying the groundwork for a national ban.

“The differences between our side of the aisle and their side of the aisle couldn’t be any clearer,” said Democratic Leader Hakeem Jeffries of New York.

Democrats criticized the resolution condemning attacks on pro-life facilities as one-sided because it did not condemn similar – and long-standing – violence against abortion clinics. The resolution is “woefully incomplete,” said New York Rep. Jerrold Nadler, the top Democrat on the House Judiciary Committee.

The Democrats argued that the legislation imposing new penalties on doctors is unnecessary because it is already illegal to kill an infant. It would create complicated new standards making it harder for health providers to do their jobs, they said.

“It is a mean-spirited solution in search of a problem,” said Rep. Judy Chu, D-Calif.

Last summer, the Democratic-led House voted to restore abortion rights nationwide, but that legislation was blocked in the closely divided Senate. That bill would have expanded on the protections Roe had previously provided by banning what supporters say are medically unnecessary restrictions that block access to safe and accessible abortions.

The Republican bills are destined to suffer a similar fate in the Senate this session. Senate Majority Leader Chuck Schumer said Americans elected Senate Democrats “to be a firewall” against what he said are Republicans’ extreme views.

“Republicans are proving how dangerously out of touch they are with mainstream America,” Schumer said.