The Virginia Tech shooter bought his guns legally though he had a mental health issue in the recent path. Virginia changed the law so that someone like him could not buy them legally now. The only problem is, they would just get them illegally or like the CT guy did and kill someone they know who has them and steal them.
Prohibition didn't work, it just gave rise to the mob which we still have today. Criminalizing drugs hasn't worked, they have been illegal for decades and can be purchased on every streetcorner in America. Outlawing guns would be no different. In fact, I would say we would be less safe as now outlaws would know we are unarmed and home invasions would skyrocket. Whenever something is illegal, there springs up an underground market for it.
On top of this, any new laws would be an extreme over reaction. Your chance of dying in a mass murder are almost nill. Your odds of being murdered by is low. Your odds of dying in a car wreck are extremely high, 1 in 84 over your lifetime. Yet nobody would give up their car.