After the jump, considering the usual remedies and an unorthodox one.
What would have prevented the tragedy?
Background check? Not in this case. The guns weren't purchased by the killer, but by the killer's mother.
Waiting period? Not in this case. The guns used had been purchased months or years before the tragedy.
Assault weapons ban? Only if the ban included, not just new sales, but confiscation of all the existing assault weapons, and owners fully complied with the ban, including the bad guys. In other words, not in this case.
Arming potential victims? Not in this case. The first victim was the woman who owned the very guns used in the tragedy.
Better mental health treatment? Not in this case. Allegedly, what set the killer off was the threat of being admitted to a mental hospital.
No, none of the usual remedies seem to be the answer in this case. That leads me to a remedy that never gets any serious consideration -- take the first clause of the Second Amendment seriously.
A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.
Source: US Constitution.
Prevent tragedies not by focusing on the gun, or on the bad guys, but on the good guys. States should reconstitute their local militias. Not the National Guard as it currently exists, but universal militia service for all citizens. Require classes in gun use, gun safety, self defense, and the law. Require frequent and regular refresher classes. Require extensive remedial classes for individuals who cannot pass tests. Mentally unstable people are very likely to be revealed in the rigorous training proposed here, in time for preventive measures to be taken.
Finally, give exemptions from militia service for anyone who voluntarily agrees not to buy, sell, own, possess, or use guns. If you're not willing to be a member of a well-regulated militia, necessary to the defense of a free state, then you'd probably be willing to voluntarily agree not to exercise your right to bear arms.
Could this have prevented the Newtown tragedy? It's only speculation, but I think it could have. Either the mother of the killer would have opted out of the militia by voluntarily agreeing not to own guns, or else her militia membership would have instilled practices that would have kept her troubled son from having access to her guns. If everyone else acted likewise (remember, we would all be in the militia), the chances are slim that the killer would have been able to gain access to the guns used in the tragedy.
The neat thing about this solution is that it is not only legal, but it restores original meaning to the Second Amendment. It doesn't impose gun regulation; it restores the well-regulated militia that the Founding Fathers called for. It finesses all the classic arguments. It has aspects to like by both the pro-gun and anti-gun factions. It doesn't even require action by the federal government. The states themselves can restore the local militias that withered away in the decades following the passage of the Second Amendment.
Even if we can't absolutely prevent every gun massacre, this solution can significantly reduce the other 30,000 gun deaths (homicides, suicides, accidents) that occur each year in America.
If we as a society don't want to give up our right to bear arms, let's at least restore our responsibility to form a well-regulated militia.