Any Republican who decides to back the legislation can argue that they just want existing laws to be enforced. And it looks like the GOP won’t have to fear backlash from the gun lobby. “We applaud Sen. John Cornyn’s efforts to ensure that the records of prohibited individuals are entered into NICS,” Chris Cox of the NRA said in a statement. “The National Rifle Association has long supported the inclusion of all legitimate records in the National Instant Criminal Background Check System.” The National Shooting Sports Foundation, a trade association for the firearms industry, put out a statement on Thursday in which it “praised U.S. Sen. John Cornyn (R-Texas) for his leadership” on the bill.

Gun control advocates support the bill too, and say it’s evidence that common ground between Republicans and Democrats in the gun debate is possible. “This is both parties affirming that there are people that we believe should not have access to guns, and we want to make sure that the system is set up in such a way that we prevent access to guns for those people,” Christian Heyne, the legislative director of the Coalition to Stop Gun Violence, which supports the legislation, said in an interview. “This is a real, genuine effort from people who couldn’t be further from each other on the other side of the aisle.”