This is just a political ploy so that a certain president and a certain party who have a big election in the fall can stand up and scream about how a certain other party "Is allowing ammunition and dangerous weapons into the hands of the mentally unstable and criminals". It has zero chance in the house.
The worst part is this would do basically nothing to stop any kind of future violence by mentally ill or unstable individuals. It wouldn't have stopped Columbine, The Gabby Giffords shooting, NIU, VA Tech or the Aurora Colorado shootings. At best it would have made the last one a little less convenient for the shooter and perhaps a little more expensive.