They could very easily talk a good game, hear back from constituents, and just go work on other things while making sure they never have to cast a vote one way or the other (where it's tick off your party hierarchy or anger your constituents).
That's politics. Nobody can come off as being callous or uncaring, so they'll pay some lip service to the idea of "doing something."
So, Mr. Politician will agree that violence is a problem and that something has to be done. He'll agree to listen to any proposal. That doesn't mean he's going to support a specific bill.