The United States has too many guns. Guns are too easy to get. There are guns for sale to the public that have no other purpose other than homicide.
While we cannot say definitively that making deadly weapons a bit more difficult to acquire (at least more difficult than a car!) would put a stop to tragedies like the one in Connecticut, they can at least make them a bit more difficult to plan and less lethal when they do occur.
If the killer had to work a little harder to buy the guns or steal them maybe there would have been time for someone to notice something. If a mental health professional could officially determine that he is potentially dangerous, he would at least have to get the guns illegally which would involve greater expense and more risk. If the guns held less ammunition there likely would have been less killing.
None of these measures remove the need to make mental health treatment more available. Nor do they deter legitimate gun owners from exercising their 2nd Amendment rights.
The point is we can take significant steps to minimize this kind of violence. What is required is the political will and a public willing to stand up for politicians who do the right thing, and against the gun lobby.