WASHINGTON - Republican U.S. Sen. John Cornyn of Texas said on Thursday that he wanted to sit down with one of the leading Senate Democrats to talk gun policy in the wake of Wednesday's mass shooting at a South Florida high school.

At a Senate Judiciary Committee hearing, U.S. Sen. Dianne Feinstein, D-California, brought the issue to the fore.

"Let’s take some action," she said. "We cannot see this continue on."

She then mentioned two areas where compromise might be reached. The first was a "Fix NICS" bill Cornyn sponsored last fall that would hold government agencies accountable for uploading relevant information to the federal background check system.

The second was related to bump stocks, which are legal firearm enhancements that allow shooters to operate firearms as if they were automatic weapons. Several Texans said last fall that they would consider banning bump stocks after the devices were found on the guns of the man who shot dozens on the Las Vegas strip. No law has since passed.

"Nobody likes these devices. You can’t have automatic weapons on the streets," Feinstein said. "It’s easy to fix. Why don’t we do it?"

The committee chairman, U.S. Sen. Charles Grassley, R-Iowa, replied: "It’s my understanding, and Sen. Cornyn brought this up to me, that the three of us are going to sit down and talk about this. Is that right?"

Feinstein said she would "love" such a meeting. Cornyn replied, "I offered to buy lunch — 0r breakfast."

But the friendly exchange did not reflect the broader sentiment at the U.S. Capitol in the hours after the shooting, as people continued to mourn the 17 people who died after a 19-year-old opened fire at the Florida high school. Several House Democrats who spoke to The Texas Tribune expressed immediate skepticism of the idea that any of the gun restriction legislation would pass with a GOP-dominated government.