It is not possible for the government to prevent Bitcoin transactions by censoring the internet. With VPNs and web-proxies being easily available, that will be unpractical. So the only option left is to block internet altogether. It is never going to happen, as there will be widespread anarchy and chaos.
I guess, the government do not have enough reasons to shutdown the internet. Censoring the use of internet will greatly affect the economy of any country considering the fact that many business nowadays depend the flows of their business transaction via internet. Many people will possibly lose their jobs and the government will not allow that to happen because the number of unemployment will increase and chaos will be experienced. If the government cannot shutdown the internet, meaning, nothing can prevent Bitcoin to be famous and patronize by everyone.
Yap because a government can gain economical gains via internet businesses by its citizen. Because most businesses are now going online it would be a disaster if a certain government were to ban any connection in world wide web. And i think they wont shut down the net with just btc as the reason. If they were to shut it down maybe by the reason that here is hacking controversy so it is not just that easy to shut down internet.