But they were far from a guarantee of a path forward for the new legislation by Senator Dianne Feinstein, especially with Majority Leader Mitch McConnell and House Speaker Paul Ryan making clear their priorities are elsewhere.
"If somebody can essentially convert a semiautomatic weapon by buying one of these and using it and cause the kind of mayhem and mass casualties that we saw in Las Vegas, that's something of obvious concern that we ought to explore," Cornyn told reporters.
"I own a lot of guns and as a hunter and sportsman I think that's our right as Americans, but I don't understand the use of this bump stock and that's another reason to have a hearing."
Cornyn later said he'd spoken with Judiciary Committee Chairman Chuck Grassley, and that Grassley was interested in convening a hearing.
The devices, known as "bump stocks" among other names, are legal and originally were intended to help people with limited hand mobility fire a semiautomatic without the individual trigger pulls required.
They can fit over the rear shoulder-stock assembly on a semiautomatic rifle and with applied pressure cause the weapon to fire continuously, increasing the rate from between 45 and 60 rounds per minute to between 400 and 800 rounds per minute, according to Feinstein's office.
The government gave its seal of approval to selling the devices in 2010 after concluding that they did not violate federal law.
At least one Republican senator, Ron Johnson of Wisconsin, said outright he was prepared to vote to ban "bump stocks." "I have no problem in banning those," he said.
Senator John Thune of South Dakota, the No. 3 Republican senator, said, "I'm interested in finding out more about bump stocks and I've got my staff looking into that and I know there are other members interested in finding out more about it as well."
Donald Trump visited Las Vegas on Wednesday but said "We're not going to talk about that today" when asked about gun issues.
