Senators are working behind the scenes on changes to a House-passed bill codifying marriage equality to get it across the finish line, Axios has learned.

Why it matters: The legislation has been mired in uncertainty since landing in the upper chamber, with just a handful of GOP senators openly stating they plan to vote for the bill — short of the 10 needed to break a filibuster.

• Most Republicans have withheld how they plan to vote, and frustrations over Democrats' steaming ahead on a major reconciliation package now threaten to boil over into other bipartisan legislation.
• Even Sen. Ron Johnson (R-Wis.), who appeared to voice support for the bill last month, suggested in an interview with Axios that he's not a firm "yes" vote: "I've never said I would support it. I said I didn't see a reason to oppose it."

Driving the news: Sen. Tammy Baldwin (D-Wis.) is working with fellow bill sponsor Sen. Susan Collins (R-Maine) to "build more support with Republicans," Baldwin's office told Axios.

• Specifically, they are discussing providing "more clarity that the legislation would not take away any religious liberty or conscience protections."
• A Senate aide close to the talks told Axios the changes would "affirm the intent of the bill, which is to maintain the status quo for the recognition of same-sex marriages in America."

What they're saying: Republican senators and aides told Axios a conference-wide discussion is underway about either proposing new language to the bill or pushing for a vote on an amendment.

• "We want to make sure that there's no infringement on your individual right or any entity's individual right to express their own beliefs from a religion standpoint," Sen. Rick Scott (R-Fla.) told Axios.
• Sen. Mitt Romney (R-Utah), a key undecided vote, told Axios he's "looking at protections for religion" as he mulls whether to vote for the bill.
• Senate aides cautioned that the discussions are in the preliminary stages.

State of play: The bill is not expected to be considered until after the August recess, as the Senate spends the next week focused on Democrats’ reconciliation package and other legislation.

• Sen. Lisa Murkowski (R-Alaska), a key vote on the measure, told Axios: "I’m not thinking about that right now. I’m thinking about the things ... that we're going to be doing this week."

The big question: Whether there is still enough precious Senate floor time to get this done.

• “Once you get into September, you’ve got to fund the government and you’ve got a bunch of other fiscal year-end issues you’ve got to deal with," Senate Minority Whip John Thune (R-S.D.) told Axios.

Be smart: Adding new language to the bill could prolong the process by requiring another House vote.

• "I don't believe it will be passed [in the Senate] in its current form," said Sen. Thom Tillis (R-N.C.), one of the bill's supporters, noting that an altered bill would "have to take another trip back over to the House."

The big picture: While polls show gay marriage has become broadly acceptable among Americans in recent years, Republicans remain less supportive.

• A Gallup poll last June found that 55% of Republicans believe gay marriage should be legal, compared with 70% of all U.S. adults.