September 13, 2022 4:24 PM EDT

Sen. Lindsey Graham of South Carolina introduced a bill on Tuesday that would ban abortions after 15 weeks of pregnancy nationwide, the biggest step by Republicans to restrict abortion on a federal level since the Supreme Court overturned Roe v. Wade.

The bill “would say after 15 weeks, no abortion on demand, except in cases of rape, incest or to save the life of the mother,” Graham said at a news conference. “That should be where America is at.”

The legislation marks a reversal for Graham, who has repeatedly said overturning Roe would allow each state to decide its policy on abortion, and argued that would be the “most constitutionally sound” way of dealing with abortion. On Tuesday, he said the new bill is meant to unify Republicans’ position on abortion and described the legislation as a response to Democrats’ failed efforts to re-establish national protections for abortion. “After they introduced the bill to define who they are, I thought it’d be nice to introduce a bill to define who we are,” Graham said.

Yet far from uniting Republicans around a shared position, Graham’s bill, called the Protecting Pain-Capable Unborn Children from Late-Term Abortions Act, exposes fissures on the right over abortion policy post-Roe. It’s an attempt to find a balance between the most conservative Republicans and activists who want to fully ban abortion and other conservatives who want to stick with more moderate limits.

He announced the bill alongside Marjorie Dannenfelser, president of Susan B. Anthony Pro-Life America, and other prominent anti-abortion leaders, and called the measure “eminently reasonable” on Tuesday. But other anti-abortion groups, such as Students for Life of America, which has advocated for more strict laws including a national ban on abortion after six weeks, did not appear with Graham. “The 15-week protection measure is not our goal, but part of a journey,” Students for Life President Kristan Hawkins said in a statement. “The Pro-Life Generation will not rest until even more lives can be saved from a tragic death even from the beginning of pregnancy.” Many leaders at the event also indicated they would like to go further, with Jeanne Mancini, president of March for Life, describing Graham’s bill as the “bare minimum” of what she would like to see.

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The measure stands almost no chance of advancing while Democrats control Congress. Graham said Tuesday that if Republicans take back the House and the Senate in the midterms, he expects a vote on the 15-week abortion ban. But Senate Republican Leader Mitch McConnell indicated shortly after Graham’s announcement that he might not want to bring the bill to a vote. “I think most of the members of my conference prefer that this be dealt with at the state level,” McConnell said.

Democrats and abortion rights advocates take issue with the framing of a 15-week ban as a middle ground for conservatives. Reproductive rights advocates critiqued the bill’s title for using the name “late-term,” a non-scientific phrase that has historically referred to abortions after at least 20 weeks of pregnancy. “15 weeks is not ‘late term,’ particularly given the significant challenges to access around the country,” Christina Reynolds, vice president of communications at Emily’s List, wrote on Twitter.

Most abortions happen before 15 weeks of pregnancy, and those that do happen beyond that point are often patients who learn they have fetal anomalies or other health problems, or those who did not know they were pregnant earlier.

Strict abortion bans are generally not popular in the U.S. A recent Pew Research Center poll showed that 62% of Americans believe abortion should be legal in all or most cases, including 38% of Republicans. And a Wall Street Journal poll conducted near the end of August found that 57% of Americans opposed banning abortion after 15 weeks if the legislation had exceptions for health of the pregnant person but not rape or incest. Graham’s bill contains exceptions for abortions “necessary to save the life of a pregnant woman,” but does not include situations that endanger the pregnant person’s health and does not allow exceptions for life-threatening “psychological or emotional conditions.” It includes exceptions for rape and incest if the patient proves they obtained counseling or medical treatment for the rape at least 48 hours before the abortion or reported the incident to law enforcement. Physicians who violate the law could face five years in prison.

The White House criticized the bill as “wildly out of step with what Americans believe” in a statement from press secretary Karine Jean-Pierre, and Senate Majority Leader Chuck Schumer called Graham’s proposal “a radical bill to institute a nationwide restriction on abortions.”

“For the hard right, this has never been about states’ rights. This has never been about letting Texas choose its own path while California takes another,” Schumer said on the Senate floor Tuesday. “For MAGA Republicans, this has always been about making abortion illegal everywhere.”

Since the Supreme Court’s decision in Dobbs v. Jackson Women’s Health Organization, about a third of states have completely banned abortion or severely restricted it, and many have enacted laws that have no exceptions for rape or incest. There have been signs of political backlash, as voters in Kansas soundly rejected a ballot initiative in August that would have amended the state’s constitution to say it did not include a right to abortion.

With measures like Graham’s, abortion opponents hope they are “moving the Overton window” of what Republicans are pitching to voters as moderate abortion bans, says Mary Ziegler, a law professor at University of California, Davis who focuses on abortion. “You can’t just pretend that politics stopped existing when Dobbs came down.”

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Write to Abigail Abrams at abigail.abrams@time.com.

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