Sen. Rand Paul, R-Ky., and the two senators who provided the most support for his talking filibuster of the drone program intend to use less dramatic means to block the Senate gun control legislation, a move the White House suggested is insensitive to the victims of gun violence.

“We will oppose the motion to proceed to any legislation that will serve as a vehicle for any additional gun restrictions,” the lawmakers wrote  to Senate Majority Harry Reid, D-Nev., in a letter on Friday.

The White House criticized the Republican senators’ decision. “To tell the families of those who lost their children to gun violence, that votes like this might be filibustered, I don’t think that would be welcome news,” White House Press Secretary Jay Carney said in a statement.

Cruz raised the specter of a national gun registry in a statement explaining his move. “The Democrats’ proposed legislation would require universal background checks for private sales between law-abiding citizens, which according to DOJ would be effective only if accompanied by a national gun registry,” he said. “This raises serious constitutional issues, and would divert resources from prosecuting felons and fugitives who try to illegally purchase guns.”

Lee’s team took a broader, process-oriented view. “Bills that potentially violate Americans’ constitutional rights should at least pass with a bipartisan majority and not be imposed by the majority alone,” communications director Brian Phillips told The Washington Examiner. “That’s why we have these rules in the Senate.”

By requiring a 60-vote threshold to end the debate, the Republicans might increase pressure on red-state Democrats who face re-election in 2014. Reid has been trying to protect them from tough votes on gun control — for instance, separated the assault weapons ban from the broader gun package, which allows some lawmakers to vote for the full bill but against the ban. But if the red-state Democrats are needed to overcome the opposition posed by Paul, Lee, and Cruz, they might have to take the kind of vote that could damage them in 2014.

“It certainly holds accountable senators who vote against the interests and principles of their constituents,” Phillips said.