Sen. Ron Johnson, a Republican from Wisconsin, departs from the Senate Chambers in the U.S. Capitol on July 21, 2022 in Washington, DC.
CNN  — 

GOP Sen. Ron Johnson, who is in a tough reelection battle in Wisconsin, indicated he would vote for a bill to codify same-sex marriage, moving supporters closer to the 60 votes needed to break a filibuster in the Senate.

In a statement, Johnson called the bill “unnecessary,” but said that if it comes up for a vote in the Senate, as it is expected to, he sees “no reason to oppose it.”

So far, five Senate Republicans are expected to vote to advance the bill – while a majority of the conference is undecided. At least 10 Republicans would need to join with Democrats to break a filibuster, but senators from both parties have said they expect the bill to eventually win 60 votes.

The Wisconsin Republican said that he does “not see any scenario in which the Supreme Court would overturn” the Obergefell v. Hodges decision and criticized Democrats for pushing a bill to codify same-sex marriage.

“The Respect for Marriage Act is another example of Democrats creating a state of fear over an issue in order to further divide Americans for their political benefit. Even though I feel the Respect for Marriage Act is unnecessary, should it come before the Senate, I see no reason to oppose it,” he said.

Senate Majority Leader Chuck Schumer took procedural steps on Thursday that would allow him to schedule debate and votes on the House-passed bill that would enshrine protections for same-sex marriages into federal law.

It’s still unclear when the votes will be scheduled, and the chances of a vote on the issue before the August recess appear grim as the Senate has a number of other priorities competing for floor time.

Schumer said on Wednesday that he wants to bring the House-passed bill to the Senate floor, and said Democrats are “working to get the necessary Senate Republicans support to ensure it would pass.”

The Democrat-led House of Representatives on Tuesday voted to pass the bill. The bipartisan final vote was 267 to 157 with 47 Republicans joining with Democrats to vote for the bill.

The House vote comes amid fears among Democrats that the conservative majority on the Supreme Court could take aim at same-sex marriage in the future, after the high court overturned Roe v. Wade in a highly consequential reversal of longstanding legal precedent.

CNN’s Ali Zaslav and Ted Barrett contributed to this report.