I have read that Arizona actually has no background check and no waiting period, and you do not need a permit to concealed carry a weapon. Since the gun was legal, technically, this guy broke his first law only once he pulled the trigger.
It is also worth remembering when discussing the Second Amendment that it does not mention guns, but arms. There is little doubt, even among the most ardent defender of the Second, that arms must be restricted. Surely no one wants mustard gas or nuclear weapons available to the general public. After all, it applied at the time to pretty much just single-shot muskets, probably less useful to a mass murderer than the bayonet stuck on the end of it (though I am in no way a Constitutional originalist: it's a stupid position and it makes Justice Scalia say some very stupid things, though he seems not so much an originalist on this issue). It seems a fair way to measure this is practical application of any weapon in terms of self-protection or sportsmanlike hunting is a fair way to regulate this. Anything specifically designed for maximum destruction: absurdly high caliber bullets that can bust an airplane hull, automatic weapons, and oversized clips are unneeded in any regard except that they are useful in maximizing damage, not unlike mustard gas, bombs or land mines (which, again, no one would argue to make legal but very extreme nuts).
Having said all that: I have seen little evidence gun control, or lack thereof, has a significant effect one way or another on violent crimes. I support the above outlines because, in situations like Arizona or Columbine, they may limit the ability of the individual(s) to do so much damage, but these restrictions will not stop attempted attack or, in any likelihood, murders of individuals. So while these restrictions have some negligible amount of potential good, I'd rather my representatives use their political influence push to revamp the health care system and save far more lives, or to ease systemic problems that lead to violence by doing things like fixing the education system, especially in poor areas.
EDIT: Also worth noting: Just as legalizing drugs would limit the violence and influence associated with illegal drug traders, or how the Prohibition created violent gangsters and its repeal was meant with them becoming less influential and violent, over-regulation of guns could create a similar violent sub-business. I am not saying all regulations are going to do this, but heavy regulations probably will. Any illegal product brings with it people, looking to make money, who are already outside the law and therefore look at things like murder and violence only in economic terms, not moral or legal ones.