We've seen how this works. He signals that he'll consider doing something sane, the media takes the bait and talks it up for days, and then we find out he's not going to do a damned thing -- except maybe make things worse. You never know, but judging from past patterns, the odds are not realistic. Via CNN:

Principal Deputy Press Secretary Raj Shah said in a statement on Monday that Trump spoke with Sen. John Cornyn, a Texas Republican, on Friday about a bill he introduced with Sen. Chris Murphy, a Connecticut Democrat, that aims to strengthen how state and federal governments report offenses that could prohibit people from buying a gun.

"While discussions are ongoing and revisions are being considered, the President is supportive of efforts to improve the federal background check system," Shah said. Students, teachers and lawmakers have urged Trump and other Republican lawmakers to take action on guns in the wake of the Parkland, Florida, shooting.

Trump, however, ran for president as a pro-gun candidate and tied himself to the National Rifle Association throughout the campaign. He also said he was open to banning bump stocks in the wake of last fall's Las Vegas shooting, but there hasn't been significant further action by the White House on that front.