Short answer: it won't do anything useful, it will be expensive, and it will further the Police State.
Long answer: It's Security Theater. Expensive, intrusive Security Theater.
The world is full of soft targets. Someone motivated to shoot up a soft target has lots of choices. There's nothing that we can do to change that.
But it gets worse. If the proper reaction to the Connecticut school shooting is to put armed police in every school, then the obvious proper reaction when an evil nut job shoots up (say) a hospital is armed police in every hospital. Then when nut jobs turn their sights on libraries, we put police there. Then grocery stores, then Starbuck's, then gas stations.
We've seen this game before, played out by the TSA: terrorists take guns onto planes and so we have metal detectors. Then they put bombs in suitcases and so all our luggage gets X-Ray'ed. Then they take bombs in their shoes and we have to take our shoes off in security. Then they use liquids and mothers can't take bottles of breast milk.
It's a stupid game and we should stop playing. There literally is no end, either to the TSA's idiocy or to Wayne LaPierre's. Actually I just lied - there is an end, and it's called a Police State. No thanks.
It's been said over and over that there are only two things that have made air travel safe in the 9/11 age: reinforced cockpit doors and passengers who know that they have to fight for their lives. It's harsh to say a week after the kids were gunned down, but the same thing applies to mass shootings. The school had locked doors, what was lacking was the ability to fight for their lives. That applies to schools, hospitals, libraries, stores, and to all the other infinitude of soft targets.
Neither the gun banners nor the NRA are willing to talk about this. And so they talk about pretty lies that are security kabuki,
It's a stupid game and we should stop playing, because lives literally are on the line.