Senate Republicans are wary of South Carolina Sen. Lindsey Graham‘s (R) introduction of legislation that would enact a national 15-week abortion ban as the party heads into the midterm elections.

They worry that Graham’s restrictive bill will turn moderate voters to the Democrats, and wonder why Graham isn’t sticking to the party’s plan of stressing the economy as the main issue.

The South Carolina senator’s bill is also surprising given new surveys that indicate growing opposition to the Supreme Court’s decision to overturn Roe v. Wade last June.

Senate Majority Leader Mitch McConnell (R-Kentucky), for one, is not onboard with Graham’s proposal.

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“With regard to his bill, you’ll have to ask him about it,” he told reporters after being asked if he would bring it to the Senate floor if Republicans win back the majority in November. “In terms of scheduling, I think most of the members of my conference prefer this be dealt with at the state level.”

Graham, however, remained confident in the bill.

“If we take back the House and the Senate, I can assure you we’ll have a vote on our bill,” he said.

Other Republican leaders, such as Senate Republican Whip John Thune (South Dakota), voiced disapproval of the bill.

“This is his idea, his decision that he’s putting out there,” Thune said, before adding, “Whether or not it ever gets voted on remains to be seen. A lot of our members believe that these are going to be issues that are debated at the state level. Individual states are going to come to a political consensus. At some point maybe there starts to become a national consensus around a sense of restrictions.”

Democrats are pouncing on Graham’s proposal, hoping to use it as leverage to keep its majority in Congress, which historically, will be a challenge.

The bill would include exceptions for rape, incest and protecting the life of the mother.

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