Sens. Tammy Baldwin and Susan Collins, the leaders pushing forward the Senate's gay marriage bill, on Thursday previewed details of an amendment to address concerns some Republicans have about its effect on religious rights. 

The effort to change the bill comes as supporters of the legislation say they're confident it can secure 10 GOP votes to clear the 60-vote filibuster threshold. But many in the GOP remain noncommittal pending a potential amendment vote. 

"We've got it essentially drafted. We're just doing some tweaks based on feedback we've had from some of our colleagues," Collins, R-Maine, said Thursday. 

Collins said she wouldn't get into specific details of the bill until Baldwin, the lead sponsor, decides to release the amendment. Collins did, however, lay out some broad areas it will address in a conversation with reporters. 

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Susan Collins speaking to reporters

Sen. Susan Collins, R-Maine, is one of the original co-sponsors of a Senate bill to protect same-sex marriage rights. (AP Photo/J. Scott Applewhite)

"We've been listening to our colleagues' concerns. And one of them has been polygamous marriages will somehow be legalized by this bill," Collins added. "In part of the bill it explicitly says that marriage has to be between two individuals. We would correct a drafting error to make that clear throughout."

Collins also said the amendment will "make sure it's not interfering with religious liberties or churches' tax-exempt status."

On the substance of the amendment, Baldwin also said that if the bill passes, "all existing precedent remains" regarding other federal laws and rights that provide religious conscience protections. 

Two potential GOP yes votes, Sens. Mitt Romney, R-Utah, and Roy Blunt, R-Mo., declined to discuss exactly what they'll need to see from an amendment to vote for the legislation. 

Sen. Baldwin speaks on Trump impeachment trial

Sen. Tammy Baldwin, D-Wis., is driving to have the Senate approve a bill protecting gay marriage rights by the end of the month or perhaps sooner. (Alex Wong/Getty Images)

"I'm working on the religious liberty issue and discussing that with the people who are leading the bill," Romney said. "We'll see whether we make sufficient progress or not."

"I'm going to look at the bill when they have a bill. I understand they're making substantial changes to it, and I look forward to seeing the changes that they're making," added Blunt.

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Blunt added that religious protections are "really important" to him. 

Baldwin said she expects the text of the amendment to be made public next week and that the legislation will be on the Senate floor "not next week but the following week."

Sen. Lindsey Graham, R-S.C.

Sen. Lindsey Graham, R-S.C., said Thursday he thinks a gay marriage bill in the Senate is "all politics" by Democrats. (Fox News)

Opponents of the legislation say it's little more than a political ploy by Democrats to attack Republicans on a social issue ahead of the midterms. 

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"The court decision stands," Sen. Lindsey Graham, R-S.C., said, referring to Obergefell v. Hodges, the Supreme Court decision that required all states to recognize same-sex marriages. "I think this is all politics." 

Congressional efforts to pass legislation protecting gay marriage rights followed a solo Supreme Court opinion by Justice Clarence Thomas in June in the case of Dobbs v. Jackson Women's Health Organization. Thomas said the court should "reconsider" its precedent on the issue. 

No other justices joined Thomas. But that opinion became a major campaign issue for Democrats and spurred lawmakers of both parties to craft legislation that would require states to recognize same-sex marriage even if that precedent eventually falls. The House passed its version earlier this summer.