Democrats say the Cornyn bill doesn’t go far enough since it includes a “probable cause” standard that would require law enforcement officials to prove that a gun buyer is an actual terrorist rather than a suspected terrorist.

Instead, Democrats want a vote on legislation that would bar firearm sales to anyone on a terrorism watch list or no-fly list.

Without a vote on their own legislation, Rep. John Lewis (D-Ga.) and other Democrats have threatened to take control of the House floor once again after they return from the Fourth of July recess. On Wednesday, Minority Leader Nancy Pelosi (D-Calif.) and dozens of other Democrats held events around the country demanding action to stop gun violence.

“House Democrats will keep up our efforts to push for the majority to allow a vote on gun violence legislation, but bringing up a bill authored by the NRA just isn’t going to cut it,” said Pelosi spokesman Drew Hammill.