Members of the U.S. Senate debated on Tuesday about the introduction of a measure that would prevent people on a federal terrorism watch list from legally purchasing handguns. Democrats proposed the measure before and after a pair of supposed radical jihadis in California last week killed more than a dozen people at a facility for the developmentally disabled.

But leaders of the Republican-controlled Senate stopped further consideration of the bill banning guns sales to suspected terrorists over a concern that the watchlist is imperfect and might violate Americans’ Second Amendment rights to purchase and own firearms. Sen. Christopher Murphy, a Democrat from Connecticut, said a growing global threat of terrorism from the Islamic State group is reason enough to “temporarily inconvenience” someone who is on the watchlist. A Democratic proposal for a watchlist includes a provision that allows an individual who is unjustly on the list to have their name removed, he said.

“I don’t think any of us [Democrats] mean to suggest that those who don’t support this bill are rooting for terrorists to get a gun,” Murphy said on Tuesday in a speech from the Senate floor. “Those who oppose this are more concerned with protecting the rights of potential terrorists than they are about taking steps to protect this country,” he added.

Majority Whip John Cornyn, a Republican senator from Texas, ended a floor discussion on the bill by accusing Democrats of “misrepresenting” the GOP position on a gun-ban watchlist. He said Democrats were trying to attach the measure to a Senate measure that would appeal the Affordable Care Act, known colloquially as Obamacare.

Under federal law, American citizens on the terrorism watchlist, also known as the “No Fly List," which bars them from boarding airlines, can legally purchase weapons because the background check mandated for gun purchases does not access the terrorism watchlist. Authorities said one of the suspects in the attack in San Bernardino, California, last week had legally purchased guns used in the massacre, but he was not on the list.