Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellMomentum growing among Republicans for Supreme Court vote before Election Day Trump expects to nominate woman to replace Ginsburg next week Video of Lindsey Graham arguing against nominating a Supreme Court justice in an election year goes viral MORE (R-Ky.) said on Monday that the Senate will vote on a 20-week abortion ban, though he didn't specify when the legislation will come up.

"It's supported by virtually all of my members, and we expect to have a vote on it at some point," McConnell told reporters during a press conference in the Rose Garden with President Trump.

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With a 52-seat majority, Republicans are unlikely to be able to pass the bill in the Senate. They would need 60 votes, including the support of at least eight Democrats, to clear the legislation.

Graham's bill currently has 45 cosponsors, none of whom are Democrats . It will be eligible for a vote through 2018, when the current Congress ends.

The legislation includes exceptions for rape if the woman received medical treatment or counseling at least 48 hours before the abortion or if she reported the rape to law enforcement.

It also includes an exception for pregnancies that result from rape or incest against a minor if it was reported to social services or law enforcement.

The House passed a similar bill largely along party lines earlier this month.