Criminal background checks for guns aren't as good of an idea as they sound. When a person has served time for a crime (especially for the largely "victimless crimes" of prostitution and drugs) we need to stop placing limitations on their rights that may hinder their re-integration in to society.
A person who was once a part of organized crime who wants to turn over a new leaf might have a very good reason for wanting a gun. And might not feel safe turing to the cops.
Lastly the many of mass shooters we find so terrifying have not had criminal records.
There is a similar issues with background checks for "mental illness" its sounds nice in theory but how exactly would that work?
Who exactly is going to be listed in a public database as "mentally ill" -- have you been treated for depression, evert been to a shrink? Maybe you have autism or maybe you saw a therapist after a death in the family. Are you then a crazy person? Should the whole world know that?
I see no way of doing this without violating the civil liberties of millions of people.
There are other ways to regulate and track guns. I support an RFID law. I support bans on semi-automatic weapons. I support the right of population centers with different needs to have different levels on gun control. I support a more robust mental health care system and above all, I support a new approach to bullying in our schools.
I do not support criminal background checks or restrictions on "crazy people" whatever that means. But most Americans, it would seem, do. And I find this VERY disturbing.