Imagine a swarm of explosive-carrying drones hitting the President's podium at inaguration from a dozen different directions. Known time, known position, open-air approaches. Must be something that keeps the Secret Service up at night.
On the other hand, you could build a cruise missile (essentially a drone) that might be big and fast enough to hit your target. But those date back to WWII, so if they keep the Secret Service up at night, it's a pretty exhausted security detail by now.
Still, people have been lifted from their beds for tweets about such things.
http://www.thesmokinggun.com/buster/obama-twitter-death-thre...
Granted that was slightly more specific threat, but this being hacker news that ggp already has a strike against ;)
It's the interceptors that would prove the most difficult to operate autonomously; they are the only one whose primary purpose is never fixed.
Rolling with the idea of a drone dystopia, as drones get smart enough you could even rely on the drone to make its own decisions and respond without an external operator.
Of course, aren't all the GPS satellites already government satellites in the first place? Seems like they wouldn't need to jam the signal, they could just shut them down, or maybe GPS can be set to require authentication...