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 shut down anything they want to shut down. It has happened before and nothing happened. Why do some government countries stops access to some sites, its because they can do it. A government in a country shut down the country's internet for hours because election is going on and they don't want citizens posting updates on the social media but the effect will be haphazard and that is one unique thing about bitcoin and why they cannot stop its penetration and reason why they are now looking for ways around it.
Not possible in any advanced country and the case for an election is temporal, on a prolonged basis, no government has what it takes to effectively shut a country out of the internet. The governments are actually helpless with Bitcoin - crytocurrency in general else long ago would they have taken it under. Something not quite obvious, is the fact that the governments that tried to stand in the way of Bitcoin actually ended up promoters of Bitcoin because people become inquisitive about Bitcoin and hardly let go after discovering it.
Yeah they can shut whatever they want down but they will lose more than they can earn by shutting down the Internet. Maybe they can not earn anything by that but they will lose more things like can not contact to anyone, it's a bit difficulty