Senate Republicans on Wednesday voiced confusion and frustration over President Donald Trump's threat not to sign a bipartisan housing affordability bill, warning that the move could undermine a rare legislative achievement and send the wrong message to voters concerned about rising living costs ahead of the midterm elections, The Hill reported.

The criticism came after Trump announced on Truth Social that he was canceling a planned signing ceremony for the 21st Century ROAD to Housing Act until Congress passes the SAVE America Act, a voting legislation measure he has described as his top legislative priority.

While Trump stopped short of explicitly threatening a veto, several Republican senators questioned the wisdom of linking the broadly supported housing measure to a bill that faces long odds in the Senate.

Texas Sen. John Cornyn called Trump's move "inexplicable," telling reporters that "I don't know if there's a precedent for it."

Maine Sen. Susan Collins was even more blunt, arguing that delaying the bill "makes no sense. This bill has very strong bipartisan support in both the House and the Senate. The primary author is a Republican senator, and it addresses an issue that affects many American families who find the cost of housing to be a tremendous burden."

The housing bill, spearheaded in the Senate by Banking Committee Chairman Sen. Tim Scott, R-S.C., passed both chambers of Congress by overwhelming bipartisan margins and has been touted by Senate Majority Leader John Thune, R-S.D., as a major legislative accomplishment, The Hill reported.

Scott declined to comment publicly on Trump's remarks.

One GOP senator, speaking on condition of anonymity to discuss the issue candidly, warned that holding up the legislation was "not a very good move."

Trump's objection centers on the SAVE America Act, which would require documented proof of citizenship for voter registration and photo identification for voting. The president has repeatedly urged Congress to pass the measure, but it lacks sufficient support to overcome a Democratic filibuster in the Senate.

Several GOP senators acknowledged that reality Wednesday.

Cornyn said he does not understand why some Republicans continue encouraging Trump to push for a vote on legislation that lacks the votes to pass.

"Ultimately, I think what the president wants to do is eliminate the filibuster, and there's not the votes to do that. At some point we have to deal with reality," Cornyn said.

He warned that continuing to focus on a bill with little chance of becoming law could hurt Republican political prospects.

"I just don't understand what they're doing, what the point is," he said. "We do have midterm elections coming up here."

Sen. Thom Tillis, R-N.C., also criticized the strategy, saying the housing legislation should move forward on its own merits.

"I don't know why you're holding a bill that's ready for signature hostage over a bill that will never pass this Congress," Tillis said. "Makes no sense to me."

Tillis argued that Democrats stand to benefit politically from Republican infighting over the issue.

"There is a huge group of people who really appreciate what the president's doing right now, and it's the Democrat Party," he added.

Despite Trump's comments, several Republicans expressed confidence that the housing bill could still become law if the president does not formally veto it. Under the Constitution, legislation sent to the White House automatically becomes law after 10 days, excluding Sundays, if the president neither signs nor vetoes it while Congress remains in session.

"I assume in 10 days it goes into law," said Oklahoma Sen. James Lankford, vice chairman of the Senate Republican Conference.

Sen. Steve Daines, R-Mont., a close ally of Senate GOP leadership, urged the administration to find a path forward.