Senate leadership will alter the bill when it comes to the floor for a marathon voting session slated to begin Wednesday, using what is known as a substitute amendment to shrink the size of the request. 

The announcement marks the first actual change planned to accommodate senators worried the cuts will undermine American influence and global public health, and could shore up Republican support ahead of a Tuesday procedural vote.

Yet the margins are expected to be narrow as members register a series of complaints about the bill, which also includes $1.1 billion in cuts to public broadcasting. Senate Majority Leader John Thune (R-SD), who can only afford to lose three Republicans on any party-line vote, remained noncommittal on whether further carveouts could be added to the substitute amendment.

“I don’t know that at this point we will,” Thune told the Washington Examiner, adding that rank-and-file members can attempt to amend the bill further on the Senate floor.

Republicans were warming to the legislation ahead of the Tuesday briefing by Vought, who has been working to address the concerns of holdouts. The Office of Management and Budget promised to protect tribal populations that rely on public radio from the broadcasting cuts, earning the vote of Sen. Mike Rounds (R-SD).

Rounds told reporters that several million dollars, a pool of money separate from the rescission request, would be redirected through the Interior Department to tribal broadcasting.

“So, it’s not a huge sum of money compared to the rest of the rescissions package, but for me, it was very important because these radio stations would not survive without that funding,” Rounds said.

Sen. Dan Sullivan (R-AK), who also represents a large Native American population in Alaska, told the Washington Examiner the compromise is “actually quite helpful,” but he would not commit to voting “yes” on the final vote.

With the changes, Republicans are more likely to support two Tuesday votes that will bring the rescissions bill to the Senate floor. But Thune, at least publicly, has yet to lock down the support needed for passage.

Sen. Susan Collins (R-ME), a top appropriator and key swing vote, said she is “grateful” that PEPFAR is being removed but signaled she still has concerns with other “problematic” parts of the bill.

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Other Republicans, including Sen. Mitch McConnell (R-KY), have registered broader complaints that the rescission request could undermine America’s “soft power” on the world stage.

Leaving the lunch, Vought predicted the rescission bill would ultimately pass before a Friday deadline to consider the request, according to CBS News. If the White House is successful, the pared-down bill would head back to the House, which narrowly passed it in June.

Ramsey Touchberry contributed to this report.