That didn't really bother me for a couple of reasons.
For one, at the moment of the takeover, the President's comments (and Gordon's response) made it pretty clear the city was largely on its own. The government would have to tread very carefully in such a situation.
Also, the movie skips through five months in about five minutes. I, too, would find it difficult to believe that the one failed covert mission was the only thing the government tried to end Bane's control. However, I find it pretty to believe/assume that the government may have tried and failed several times during the five months but that we just didn't see it.