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.
Government can easily shut down any site they desire to. They have this so called power that will work to literally everyone. And in my personal opinion, if government starts to fire an issue that internet will be completely shut down, everyone will go against it, we at least 70% of the human being who are internet users.