Indeed. Appropriate reactions include, but are not limited to:
1) Rage-quit
2) Despair
3) Disbelief
4) Pleading
5) Save-scumming
6) (╯°□°)╯︵ ┻━┻
7) Taking a long walk and thinking about your life
8.) Pulling all the levers
9) Abandoning immediately
10) Hope.
If you don't save-scum, you're in for a bumpy ride: I recommend healthy doses of 10 (Hope). Try isolating affected dwarves and letting them kill each other (ones with descriptions calling them enemies of the fort, enemies of the civ, or both are affected), ideally activating them (and them alone!) so they attack more. If at any point they stop killing each other, they might be all on the same side; if that side is one completely the enemy of your fort, your soldiers should be able to attack them without becoming an enemy and setting off a problem.
A safe thing would be just to start hiding off citizens (i.e. ones who don't have any "Is an enemy of [insert your fort or civ here]" in their description) off somewhere while others die off. Do not turn on the military of citizens if you do this, because then they will attack their enemies (and thus may end up enemies themselves). Most of these insurrections are spread by military fights, since civilians (of any loyalty) usually run from enemies while the military engage. (which, however, means civilians don't necessarily show whether or not they are affected, since most of the time all you'll get is a cancellation notice from dwarves fleeing the "enemy". Thus they can lull you into a false sense of security).
This can be survived, but there is a strong possibility depending on how far along it is that you'll be left with 10 or fewer civilian dwarfs who'll ignore your commands and eventually get killed in the next attack (read: pray for migrants).
EDIT: Oh hey, the wiki was updated with my research on that! Neat. Will almost certainly be irrelevant in the next version with the new way of handling loyalty (to, in Toady's words, probably be replaced with new and exciting problems!), but still. Covers most of what's in this post though.