The problem is the statement of barring access to criminals.
Prior to the shooting in Aurora, James Holmes had not committed any crime involving a firearm until the point where he left his apartment with the intent to murder others. The exact timing of when that became a crime might be under debate, but the fact is that up until he started shooting, there was nothing indicating he had illegal intent.
The police or feds are not omnipotent. We can't predict people who have bad intentions and even if we could there would be no way to tell if anyone would really follow through.
We can have a "national discussion", but usually what that means out of a politicians mouth is they want to pass a law. Of course they do, it's the only solution they have. We have enough laws. We have MORE than enough laws. If the current laws are deemed ineffective, then the proper action would be to repeal some of the current laws and replace them with something more effective.
That never happens in the USA though. They just make more behavior illegal.
There have been many stories, albeit buried by the mainstream media, of potential mass shootings that were stopped by those wielding firearms.
Maybe what we need to ask is how do we stop these shootings in gun free zones? Even that won't stop the whole problem. Just ask Rep. Giffords.
We are not going to stop murder in this country. We can either allow people to defend themselves or make them easier targets.