Can the government shut down the internet? Yes they can!
First, why do you think this?
actually you can do that (like north korea). but then: welcome to the stoneage!
and in 5-10 years there will be alot of sattelites which will bring the internet (and Bitcoin) in every corner of the world.
(there will be even BITCOIN SATELLITES
)http://www.coindesk.com/bitcoin-nanosatellites-orbit-earth-2016/