U.S. Sen. John Cornyn, R-Texas, has enough support to pass his “Fix NICS” gun control bill without the possibility of a filibuster, his office said Friday morning.

It’s not yet clear when the bill might get a vote, but a staff member said there are now 62 sponsors of the bill — a significant milestone. The bill would hold government agencies accountable for failing to properly document individuals’ criminal histories in the FBI’s National Instant Criminal Background Check System.

Cornyn and U.S. Sen. Chris Murphy, D-Conn., first launched that bill in November after the Sutherland Springs shooting that killed more than two dozen people. But it has stalled in the Senate since then, despite having dozens of senators sign on as co-sponsors recent weeks.

The bill has bipartisan support, though Texas' other U.S. senator, Republican Ted Cruz, is not among the co-sponsors.

Earlier this week on the Senate floor, Cornyn implored his colleagues to pass the bill.

"We should start with what's achievable and what will actually save lives, and that describes the Fix NICS bill," he said. "It will help prevent dangerous individuals with criminal convictions and a history of mental illness from buying firearms.”

Cornyn added, "This bill could easily pass the Senate. It's already passed the House. And the president would sign it, as he told me when he called me last Thursday night.”

The NICS database, which is maintained by the FBI, came into public focus last fall after former U.S. Air Force airman Devin Kelley opened fire at a Texas church, killing 26. The Air Force revealed after the shooting that it had failed to report the gunman's history of domestic assault to the database. That information should have prevented him from purchasing a gun.

Cornyn's bill would require federal agencies and states to design plans for ensuring information is accurately reported to the database, and it would allocate resources to those agencies to help them do so. It would also set up a system of incentives and penalties for agencies who comply or fail to comply.