Sen. Chris Murphy (D., Conn.) couldn't say Thursday whether the gun control laws Senate Democrats are pushing in Congress would have stopped the Orlando terrorist from carrying out his massacre.

Murphy, with the help of other Democrats, filibustered for nearly 15 hours beginning Wednesday. He ended it early Thursday morning with the announcement that the GOP-led chamber would allow votes on whether to ban people on the terror watch list to buy guns, as well as expanding background checks to Internet sales and gun shows.

"Would any of the legislation that you're supporting have prevented the shooter in Orlando, the shooter in San Bernardino, or the shooter in Newtown from purchasing a gun?" CBS This Morning host Norah O'Donnell asked.

"So it's certainly a question as to whether this may have been impactful in Orlando," Murphy said. "What this legislation Senator Feinstein has offered would allow is for the FBI to put individuals on the list of those who can't buy weapons if they suspect they are linked to terrorist organizations."

The Orlando killer, Omar Mateen, had previously been on a terrorist watch list but was taken off it before the killings.

"But as you know, if someone is currently on a terror watchlist and goes to buy a gun, the FBI director said they are notified. There is an alert sent," O'Donnell said.

"So there's an alert sent, but there's no prohibition on that individual walking out of the store with a weapon, and the fact is in this case, the time between the purchase of the weapon and the attack was fairly short," Murphy said. "So if we have made a decision that the people on these lists can't get on a plane … why don't we also make a decision that they can't get a weapon?

"I think that there's a question, if this place had been in place, would it have been impactful in Orlando? It might have been, and I think that's one of the reasons it's worthy to go forward."

Co-host Gayle King, who previously asked what it would take to get gun control passed in an interview with Homeland Security Secretary Jeh Johnson, told Murphy "many people are applauding you for raising the issue again."

The White House similarly could not name a single mass shooting that would have been prevented by proposed gun control legislation last year.