Proper training can sometimes be a lifesaver, but it's not some magic answer. It's not at all unusual for police to be killed in the line of duty - armed, trained, and usually alert.
Any idea that if we just change one thing the problem will go away is, in my opinion, misguided. Instead, reasonable and sane action on several fronts will help, but not not solve, the problem. To do nothing because any one action isn't the complete answer is fool-hardy, though, I think
We do have some useful data that can guide the public dialogue. Many countries have some form of gun control - it would seem obvious to track what has happened there, and learn what does and does not work. We also know something about what can happen when there is a gun in a household - while by no means is there injury in every armed household, if someone IS injured, the chances are much higher that it will be a member of the household, not some intruder or enemy.
The idea from the NRA yesterday about armed guards at every school strikes me as the height of folly. There are not unlimited funds for this, so who would be hired? Poorly trained and poorly vetted individuals, especially in poorer districts. As a parent, I do not find the idea of the kind of person who would be attracted to strutting around a school with a gun on his hip reassuring. What happened in Connecticut is appalling, but it doesn't change the reality that most children are not harmed by a crazed stranger, but by someone close to them with some authority over them. I'd personally be a lot more afraid of those guards, looking at it statistically.