(CNN) — Senate Majority Leader Chuck Schumer said on Wednesday that he intends to hold a vote on a bill to codify same-sex marriage into federal law "in the coming weeks," and hopes there will be enough Republican support to pass it.
Schumer also said he would prefer to bring it to the floor as a separate piece of legislation, and not attached to a must-pass government funding bill.
"Let me be clear a vote will happen -- a vote on marriage equality will happen on the Senate floor in the coming weeks, and I hope there will be 10 Republicans to support it," Schumer said at a news conference on Capitol Hill.
The Senate returned to Washington after the August recess this week and Democrats, who control the chamber, must decide how and when to hold votes on several key items ahead of the upcoming November midterm elections where control of Congress is at stake.
The main must-pass legislative item on the to-do list is a bill to extend government funding past a September 30 deadline and avert a shutdown, but Democrats are also pushing to hold a vote on same-sex marriage. There have been questions over whether the same-sex marriage bill could be attached to the government funding measure, but prominent supporters of the bill have pushed back and argued it should take place as a stand-alone vote.
Schumer on Wednesday said of the same-sex marriage legislation, "we would prefer to do it as a separate bill. We hope there are 10 Republicans to help us with that," when asked if it would be attached to a must-pass government funding bill.
Senate Appropriations Chairman Patrick Leahy told reporters on Wednesday that same-sex marriage legislation will not be included in the continuing resolution, otherwise known as a "CR" -- a short-term government funding package to avert a shutdown.
"Not going to happen," the Vermont Democrat said of adding the bill to the funding measure.
Senate Minority Leader Mitch McConnell also expressed support for a "clean" stop-gap bill to extend government funding at a separate news conference, implying that additional items should not be attached, though he did not specifically reference the same-sex marriage bill.
"I think the key to getting the CR done with the least amount of controversy is for it to be as clean as possible," he said.
Momentum -- and support -- has picked up on Capitol Hill for a Senate vote on a bill to codify same-sex marriage after the Supreme Court overturned Roe v. Wade in June. The Democrat-led House of Representatives passed a bill to enshrine protections for same-sex marriage into federal law in July, amid fears among Democrats that the conservative majority on the Supreme Court could take aim at same-sex marriage in the future.
Democrats could use the issue to force a tough vote for vulnerable Republicans up for reelection in November, but it's still not clear if the necessary support would ultimately be there to pass the legislation. At least 10 Republicans would have to vote with all Democrats to overcome a filibuster and pass the legislation.
Democratic Sen. Tammy Baldwin said that they are "darn close" to getting 10 Republicans on board.
Asked if the bill could come to the floor before the midterms, Baldwin said, "Oh, absolutely," and she added that folding it into the continuing resolution to fund the government is "not my preferred route."
"I think we should have a vote sooner rather than later," she said.
Concerns over religious liberty
Republican Sen. Ron Johnson of Wisconsin, who had previously signaled he would vote in favor of a bill codifying same-sex marriage, said Wednesday that he now cannot support it as written, citing concerns over religious liberty.
"Not in its current form," he told CNN when asked if he still supports the bill.
"There have been very serious issues raised about religious liberty, and I'll take those seriously," Johnson said as he boarded an elevator in the Capitol, adding that he was working with other senators to find new language that could be added by amendment to satisfy their concerns.
A bipartisan group of negotiators -- working to get at least 60 votes for the bill -- is considering adding language to the bill to address concerns of critics, but it's unclear if what they may come up with would satisfy Johnson.
Johnson is in a tight reelection race in Wisconsin. Previously, he had said he didn't think the new law was necessary and Democrats were pushing for its passage for political reasons, but nevertheless signaled he would back it. "Even though I feel the Respect for Marriage Act is unnecessary, should it come before the Senate, I see no reason to oppose it," Johnson said in July.
Another Republican, Sen. Todd Young of Indiana, said he is still weighing the legislation and also cited religious liberty concerns.
"I don't think government should play any role whatsoever in sanctioning what for, you know, hundreds of millions of Americans are a religious sacrament," said Young, who is up for reelection. "But that's not the choice I'll be offered if this comes before the Senate. I do understand that. And so I haven't made up my final mind about any legislative text, because I don't think the text has been finalized and because I'm still consulting with my constituents on this matter."
This story has been updated with additional developments Wednesday.
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