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/
Wasn't there a group that was attempting to transmit the blockchain through RF?
A Finnish group if I am not mistaken.
They said they were working on ways to make it a two way transmission too.