It's all well and good saying 'gun control' and 'banning guns' but how do you retrieve the 300 million plus guns already in circulation? There are no registries, there are no records to say where it is or who has it, just the point of sale transaction. New Zealand are currently dealing with the same issue, making certain guns illegal outright and asking people to hand them in, some people will, some people won't.
Banning handguns in the UK was easy, all firearms are registered on a license, along with address and legal owner. The powers that be can (and did) simply went to the registered addresses and forced their purchase / turn in. That is simply impossible in the US. As someone else said previously, the culture is so entrenched and has been for so long that there simply is no way to legislate itself out of trouble. Any new laws making things difficult to get hold of are circumvented by the sheer number of them already in circulation.
Integrating better and more thorough checks and actually utilizing the laws already in place (mental health referrals, communication between health professionals etc) will be a big help.