Story highlights Consensus has been building to outlaw bump stocks that modify guns

However, some are pushing for an ATF regulation change, not a new law

(CNN) The next fight in the gun debate isn't over what to do, but who should do it.

Capitol Hill Republicans have opened the door to regulating bump fire stocks, gun accessories that can convert semi-automatic weapons into firing similarly to automatic ones, but the scope of those changes, the timing and who ultimately will make them is still a major question on Capitol Hill.

After the deadliest shooting in modern American history, Republican leaders have signaled some openness to at least looking into narrowly addressing the country's existing gun laws. The Senate's No. 2 Republican Sen. John Cornyn told reporters he wanted to see a hearing when the Las Vegas shooting investigation concluded.

House Speaker Paul Ryan, an avid outdoorsman and hunter, told reporters Thursday that bump stocks were something that the country should consider taking a look at.

"We all have to get more educated as to what these are, how it -- how they became available in the first place. Was it a regulatory misstep by ATF some number of years ago? And we all know and believe that fully auto weapons are illegal, and so is this a big gap that needs to be closed, and if so how to close it. That's -- we're all just beginning to go through that analysis," he said.