Security at military bases is certainly tighter than most places, but it only goes so far. Only very high value places will have security at or above TSA-levels. Base security is put in place mainly to deter and to detect people trying to con their way inside. Someone legitimately stationed there, who travels through security frequently, and has all the proper credentials normally wouldn't have a hard time sneaking something small through a main gate.
There are times when security is tightened at random intervals, but most of these are impractical for permanent operations.
The Brady campaign and others are already trying to drum up support, but I think their arguments are fairly easy to refute. How do most mass shootings end, when the shooter doesn't commit suicide? It's usually by a "good guy" with a firearm.
At this point, I'm more worried about the 1st Amendment implications. I've seen more than a few comments about taking actions against Muslims, and many don't pass Constitutional muster. We need to remain vigilant against these knee-jerk reactions.