Senate Democrats are pushing to pass a law codifying same-sex marriage in September, putting Senate Republicans in a precarious situation. Votes to support or oppose the measure will both come with risks: of alienating either a majority of voters or a swath of the GOP’s base.

Senator Baldwin, a Democrat, will help gather support for the Respect for Marriage Act in the Senate, taking the torch from Congressman Jerold Nadler, who sponsored the bill in the House.

The bill would codify in federal law protections currently afforded to same-sex and interracial couples by Supreme Court rulings. Its main effect would be repealing the 1996 Defense of Marriage Act, which establishes that the federal definition of marriage is “a legal union between one man and one woman” and that a spouse is “only a person of the opposite sex.” 

So far, four Senate Republicans have said they would support the bill — Senators Murkowski, Tillis, Collins, and Portman. Senator Johnson of Wisconsin has said that he sees “no reason to oppose it,” which has been widely interpreted as support.

Eight Republicans have said they would oppose it: Senators Rubio, Cruz, Graham, Hawley, Inhofe, Coryn, Cassidy, and Wicker. The 37 remaining Republican senators have so far been mum on the issue. 

Gallup polling from June of this year shows that support for same-sex marriage in America is higher than ever — 71 percent — but that the Republican Party remains divided on the issue, with 55 percent of GOP voters supporting it.

The vote would put Senate Republicans in the unenviable position of needing to navigate the issue without alienating the the majority of voters who support same-sex marriage or the portion of their base who oppose it.

The quandary is perhaps best illustrated by Mr. Rubio’s position. The senator chose to oppose the bill despite some 76 percent of Floridians saying they support same-sex marriage, according to a Pew Research survey.

His refusal to sign on will likely become a talking point for his opponent, Congresswoman Val Demings, who is challenging the incumbent senator in November.

The director of the Florida State University Institute of Politics, Hans Hassell, says Mr. Rubio will likely try to brush off the vote.

“It seems that Rubio’s position is a ‘no,’ but is also that it’s a ‘stupid waste of time,’” Mr. Hassell said. “Politicians’ explanations of unpopular votes are often very effective at mitigating any potential negative effects those votes might have, and I suspect this will be similar.”

The issue has been the subject of renewed interest following the Dobbs v. Jackson decision that overturned Roe v. Wade, which has made abortion a decisive issue in this year’s midterm elections.

In his concurring opinion in Dobbs, Justice Clarence Thomas wrote that the Supreme Court also should review, among other rulings, Obergefell v. Hodges, the landmark 2015 case that legalized same-sex marriage nationally.

If the Supreme Court were to overturn the Obergefell ruling, the issue would likely be kicked back to the states, as abortion was, resulting in some bans on same-sex marriage going into effect.

In Florida, for example, same-sex marriage was banned until a 2014 district court ruling declaring it unconstitutional. The law, however, remains on the books.

A ruling from the Supreme Court could result in the ban being reinstated, an eventuality that Democrats could campaign on should the bill fail. If the Democratic successes following the Dobbs decision are a lesson, same-sex marriage would be a potent talking point for Democrats.

Ms. Baldwin says she is confident that she will be able to rally 60 senators in support of the bill and that her Republican colleagues simply prefer to keep their position private ahead of the vote.

Pass or fail, the bill could mark another win for Democrats, who will be able to either add it to a growing list of accomplishments going into the midterms or campaign against stubborn Republican opposition to the popular measure.