So far, the best, and in my mind the most Constitutionally acceptable response to the Newtown Massacre that I've seen is legislating a requirement that gun owners carry insurance on their firearms. Insurance rates could be set by private insurers using actuarial tables. What you would pay would be based on the type of firearm, the likelihood of its use in a crime, etc.
For example, I own three guns, a reproduction musket, an antique bolt action rifle, and a five-shot snub-nosed revolver. I'd expect that the revolver would be the costliest of my three weapons to insure, based on its concealablity and greater likelihood to be used in a crime if lost or stolen. The rifle and musket likely have a much lesser propensity for violence, especially the musket, due to its unwieldiness and slow reloading time.
I think this is a workable solution. It doesn't unduly burden those purchasing weapons for hunting or home defense, while preserving the ability for people to purchase high ammo capacity semi-automatic military grade weapons if they wish to own them, they just have to pay more to insure it the same way it costs more to insure a high-performance sports car as compared to a family sedan. Discounts can also be offered for those who use trigger locks and store the ammunition separately, just as homeowners get a discount for having smoke detectors. Since the insurance would be provided by private companies, anti-government paranoids wouldn't have to worry that the gubmit is tracking their guns.
I think this is also a solution to straw man purchasers. A straw purchaser would have to get insurance for the weapon, even though they no longer possess it. No one is going to want to maintain insurance on a weapon that they've illegally turned over to a third party.
UPDATE: Three dead in central PA.