In "Dark Knight Rises" what was U.S. government's strategy?

Toward the end of Dark Knight Rises, the biggest city in the United States has been held hostage for nearly five months. Bane has threatened to destroy the city via nuke if anyone leaves the city. Bane has also explained to the world how the nuke is going to detonate on its own after five months (update on this last sentence: apparently Bane did not announce the five-months thing -- only a handful of characters were aware of it).

So at some point, perhaps as the five months was almost over, wouldn't the US government have nothing to lose by directing the military to try some sort of raid? Given Bane's army consisted mainly of homeless teens with small arms, seems like the world's most advanced military could probably have put together more than one plan-of-attack to choose from, especially with five months to think about it -- and the military would probably be eager to take a shot at saving millions of citizens from obliteration.

Why would the U.S. government let the nuke detonate without even trying to stop it?