A proposal by Sen. Lindsey Graham to ban abortion after 15 weeks has highlighted the stark differences among Senate Republicans on abortion, with Senate Minority Leader Mitch McConnell telling reporters Tuesday that most members of his conference would prefer the issue “be dealt with on a state level.”

Graham, R-S.C.,  who has long advocated for legislation that would prohibit abortions after 20 weeks of pregnancy, introduced his bill Tuesday alongside leadership from some of the nation’s largest anti-abortion advocacy groups, including March for Life and Susan B. Anthony Pro-Life America. The legislation would ban most abortions after 15 weeks but include exceptions for rape, incest and to protect the life and physical health of the mother.

“We have made the decision as a group here,” said Graham, referring to the advocates. “You’ve got issues at the state level, you’ve got issues at the federal level. We’re trying to pick a position we think will rally the country to be more sympathetic to an unborn child.”

But his bill, introduced just two months before the November midterms, may be complicated for his fellow Republicans. Since the June 24 Supreme Court decision overturning Roe v. Wade, Republicans have largely limited their legislative pushes on the issue to the state level.

Some Republican strategists have warned against focusing on abortion messaging after Kansas voters overwhelmingly defeated a ballot initiative this year that would have added language to the state constitution that abortion was not a constitutional right.

McConnell similarly shied away from a unifying message for Republican senators up for reelection.

“I think every Republican senator running this year in these contested races has an answer to how they feel about the issue. It may be different in different states. I leave it up to our candidates who are quite capable of handling this issue to determine for them what their response is,” he said.

In contrast, Democrats have rallied around federal abortion rights legislation during the increasingly heated lead-up to November, voting on bills that would codify abortion rights, protect interstate travel to seek abortions and protect access to contraception.

Senate Democrats, meanwhile, stymied by their thin margins, have held procedural votes on codifying abortion rights that have not passed.

On Tuesday, Democrats sent out a flurry of reactions to Graham’s bill, with White House Press Secretary Karine Jean-Pierre saying the bill “is wildly out of step with what Americans believe” and Speaker Nancy Pelosi calling the bill “the latest, clearest signal of extreme MAGA Republicans’ intent to criminalize women’s health freedom in all 50 states and arrest doctors for providing basic care.”

Both parties have traditionally held votes on abortion policy when they hold control, but the votes have been largely stymied because of Senate filibuster rules. Mostly, they’re considered a messaging strategy to either parties’ base, often timed around specific events.

Graham, speaking at his own news conference, disagreed that messaging on his bill would be harmful to those up for election.

“What I’m trying to tell my colleagues is that there is a consensus view from most prominent pro-life groups in America that this is where America should be at the federal level. I don’t think this is going to hurt us,” said Graham.

Graham’s push for this bill comes even after he called for all abortion policy to fall to the state level during a June interview with Fox News.

“All of us in the conservative world have believed that there’s nothing in the Constitution giving the federal government the right to regulate abortion. There’s nothing in the Constitution that creates a right to abortion as a constitutional principle,” he said then.

Senate Majority Leader Charles E. Schumer, D-N.Y., and Senate Assistant Democratic Leader Patty Murray, D-Wash., both spoke out against Graham for bringing up the federal limit.

“Republicans are twisting themselves into pretzels trying to explain why they want nationwide abortion bans when they said they’d leave it up to the states,” Schumer said on the Senate floor Tuesday. “For the hard right, this has never been about states’ rights.”