The Respect for Marriage Act, which would enshrine federal protections for same-sex marriage, is moving forward in the Senate following a 62-to-37 Wednesday vote in favor of advancing the bill. Twelve GOP senators joined their Democratic colleagues to vote in favor of the measure.

The vote is a procedural maneuver needed to advance the bill, which supporters are hoping to do in a timely manner. Ahead of the vote, the bill’s supporters claimed to have a filibuster-proof majority.

The bill aims to repeal the 1996 Defense of Marriage Act and would require states to recognize marriages performed in other states. Although some opposed to the bill said it would legalize polygamy, it would not.

The majority leader, Senator Schumer, said Tuesday that he hopes the bill can move forward quickly after this first vote. A similar bill passed the House this summer with 47 Republican votes.

The bill has also gained one notable supporter outside of Congress — the Church of Jesus Christ of Latter-day Saints. The church announced Tuesday that it is supporting the legislation.

The church’s stipulation is that it pass with the necessary provisions to protect same-sex marriage, as well as “appropriate religious freedom protections,” according to a statement.

The church still maintains that same-sex relations are against God’s commandments, but stated that it will work to “preserve the principles and practices of religious freedom together with the rights of LGBTQ individuals.”

The statement from the church has given cover to Senator Romney, who told Politico he would support the bill “if it includes important protections for religions and religious institutions.”

Mr. Romney is the latest Republican to support the bill. Senators Collins, Portman, and Tillis expressed support for the bill in a joint statement issued Monday.

“The Respect for Marriage Act is a needed step to provide millions of loving couples in same-sex and interracial marriages the certainty that they will continue to enjoy the freedoms, rights, and responsibilities afforded to all other marriages,” the senators wrote.

The new amendment explicitly protects “all religious liberty and conscience protections under the Constitution or Federal law” according to supporters of the bill.

The new amendment also confirms that nonprofit religious organizations “will not be required to provide any services, facilities, or goods for the solemnization or celebration of a marriage.”

With the new amendment, the bill will need to pass the Senate after the differences with the House bill are worked out. Then both bodies will vote on the final bill.  Mr. Schumer expects that the legislation will pass after Thanksgiving, and President Biden is widely expected to sign it without reservation.

Before Wednesday’s vote, there were only 54 senators publicly supporting the bill, making the 62 votes in favor of advancing it a surprise.

The bill in question was introduced in response to fears that the Supreme Court could overturn a legal precedent protecting same-sex marriage at the federal level after Justice Clarence Thomas specifically mentioned reconsidering the topic in his opinion in Dobbs v. Jackson.

Some members of the Republican conference have criticized the bill, saying that it is not necessary or that it shouldn’t be passed in a lame-duck session.

The bill was under consideration earlier this year, but Senate Democrats moved the vote until after the midterms, fearing that some legislators might be less inclined to support the bill before an election.