The only reason people mine bitcoin is because they can either spend it or convert it to fiat. 

The only reason merchants accept it, is because they can convert it to fiat. 

If you shut down the exchanges bitcoin will die. The only way this wont happen is if the merchants suppliers will also except bitcoin and you can basically spend it everywhere for everything, then it truly does become a worldwide currency in its own right.

It would be impossible for every exchange in every country of the world to be shut down - there will always be one and if there is one there is a way!

Long and short of it is - the government cant destroy bitcoin through any of the above means.

There is however one sure-fire way the government can destroy the currency and that is to destroy peoples confidence it...

Crack SHA-256, make it public - show the coin as vulnerable and insecure - who would even want to use it then?