Senate Majority Leader John Thune, R-S.D., on Tuesday dashed a push from President Donald Trump and his allies to amend the Senate filibuster rule to speed passing controversial voter-identification legislation.

The SAVE America Act, which was introduced in January, would require voters to prove their citizenship to register to vote in federal elections and would require certain forms of photo ID to cast a ballot. The measure is slated for a vote in the House this week but faces an uphill climb in the Senate where Democrats have vowed to use the filibuster to block the legislation, which they say could disenfranchise millions of Americans. Because of the filibuster rule, bills require 60 votes to advance in the Senate.

Proponents of the voter-ID legislation are calling for changes to the chamber’s rules.

“There aren’t anywhere close to the votes, not even close, to nuking the filibuster,” Thune said at a press conference following a meeting of Senate Republicans on Tuesday. “So that idea is something, although it continues to be put out there. … That doesn’t have a future.”

Sen. Mike Lee, R-Utah, who is leading the push for the bill in the Senate, has called to abolish the so-called “zombie filibuster” and bring back an older form of the rule that requires objecting members to be physically on the floor and talking to delay legislation.