Thune’s comments came as Senate Republicans discussed the strategy during a closed-door lunch meeting. The proposal would require Democrats to continuously hold the Senate floor and debate the legislation to block it, potentially extending debate for days or weeks.

The legislation, known as the Safeguard American Voter Eligibility (SAVE) Act, has been identified as a top priority by President Donald Trump, who raised the issue Monday during a policy meeting with House Republicans.

Speaking in Florida earlier that day, Trump said passage of the SAVE Act was important to Republican efforts to maintain control of Congress in the upcoming November elections. “It will guarantee the midterms. If you don’t get it, big trouble,” he said, per The Hill.

Democrats have argued that only a small number of cases involving immigrants in the country illegally voting in federal elections have been documented in recent years, and they falsely say available evidence does not support claims of widespread voter fraud.

At the same time, President Donald Trump has increased pressure on Senate Republican leaders to adopt the talking filibuster strategy to advance the Safeguard American Voter Eligibility Act. Trump has also withheld an endorsement in the closely watched Republican Senate primary in Texas between John Cornyn and Ken Paxton.

Thune and other Republican leaders have encouraged Trump to back Cornyn, arguing that he may have a stronger chance of winning the general election. However, Trump has not yet announced his support for either candidate.

Asked about speculation that the White House may be delaying an endorsement because Trump disagrees with Senate Republicans over the talking filibuster approach, Thune acknowledged the possibility and said it was a concern.

“Yeah, I mean, that’s probably not a linkage that is in anybody’s best interest because voting on the SAVE America Act is something we can do but passage is not guaranteed,” Thune said, per The Hill. “You have to make political decisions independent of what the final disposition of that might be on the floor.”

Supporters of the talking filibuster strategy in the Senate, including Sens. Mike Lee (R-Utah) and Rick Scott (R-Fla.), argue that the approach could help advance the Safeguard American Voter Eligibility Act. They say requiring Democrats to continuously debate the bill on the Senate floor could increase pressure to allow it to pass by a simple majority vote.

Lee outlined the case for the strategy during a meeting with Republican senators on Tuesday. Advocates say the extended debate could eventually exhaust opposition and lead to a vote on the legislation.

However, other Republican senators, including Senate Majority Leader John Thune, have expressed skepticism about the approach. They warn that forcing a prolonged debate could instead stall the Senate’s work for weeks or months without producing a legislative breakthrough, The Hill noted.

Thune said his staff had been unable to identify any historical example in which legislation passed by relying on a similar strategy involving numerous procedural votes and extended floor debate to overcome opposition.

Trump said Sunday that he will not sign any bills until the SAVE America Act is passed, adding that a “watered down” version of the act wouldn’t suffice.

“It supersedes everything else. MUST GO TO THE FRONT OF THE LINE. I, as President, will not sign other Bills until this is passed, AND NOT THE WATERED DOWN VERSION — GO FOR THE GOLD: MUST SHOW VOTER I.D. & PROOF OF CITIZENSHIP: NO MAIL-IN BALLOTS EXCEPT FOR MILITARY — ILLNESS, DISABILITY, TRAVEL: NO MEN IN WOMEN’S SPORTS: NO TRANSGENDER MUTILIZATION FOR CHILDREN! DO NOT FAIL!!!” Trump wrote on Truth Social.

“I would close government over it,” Trump said. “To me, that’s a core belief.”