The case is certain to inject the divisive politics of abortion into the 2020 presidential race. President Trump ran and won in 2016 partly on a promise to nominate Supreme Court justices who would overturn Roe, and June Medical is the court’s first case on abortion since Justices Neil M. Gorsuch and Brett M. Kavanaugh, both appointed by Mr. Trump, joined the court.

The sheer number of those signing the brief suggests the importance that Republicans place on restricting abortion rights and telegraphing to their core supporters that they are serious about doing so. The signers include the top three House Republicans — Representatives Kevin McCarthy of California, Steve Scalise of Louisiana and Liz Cheney of Wyoming — and the No. 2 Senate Republican, John Thune of South Dakota.

But Senator Mitch McConnell, Republican of Kentucky and the majority leader, did not sign. Nor did several Republicans facing challenging re-election contests in politically competitive states, including Senators Susan Collins of Maine, Cory Gardner of Colorado and Martha McSally of Arizona. The two Democrats who signed, Representatives Collin C. Peterson of Minnesota and Daniel Lipinski of Illinois, are both from the party’s conservative wing. Mr. Peterson broke with Democrats last month in voting against impeaching Mr. Trump, and Mr. Lipinski’s stance against abortion rights has prompted internal strife within the party.

The brief was drafted by Americans United for Life, an anti-abortion-rights group. Katie Glenn, a lawyer for the organization, said that when the court took the case, members of Congress wanted to weigh in. But, she said, they are aware that overturning Roe would be a huge leap, even for a court that is moving to the right.

“No one is going into this case with an expectation that Roe v. Wade will be overturned,” Ms. Glenn said. “However, the court has the opportunity to reconsider the precedent that has gotten us to where we’re at, and that’s all that the members of Congress were seeking to point out, that it is the court’s prerogative to assess the jurisprudence that got us here.”