I don't have an answer for this one.
I just finished Justin Cronin's The Passage (my negative review here), which hits a bunch of "government bad" tropes: the US government surveils intrusively; can't prevent terrorism; can't rebuild storm-ravaged New Orleans; funds secret experiments; kidnaps children; unwittingly unleashes a plague of vampires on the world. And then, in the post-vampire apocalypse, the fictional government we see has a much smaller scope (a colony of a hundred people), but hardly inspires trust.
Actually, how many fictional apocalypses do you think have government roots? Probably more than the apocalypses that are rooted in private action. (Off the top of my head, I can only think of one privately-caused apocalypse: Ward Moore's Greener Than You Think. There's got to be more, though, right?)
But what about non-apocalyptic situations in fiction: does government work in a day-to-day capacity? Or is it too hopelessly corrupt and too baroquely complex to do any work?
(Although here's a thought: once we include "police" as a category of government, does the rate of successful work go up?)