Governments (aside from the insane despotic ones, perhaps) won't literally "shut down" the internet, because communications infrastructure is a necessary part of a modern society. Our economy wouldn't function without it.

Regulating the internet more heavily is certainly a possibility, though. e.g setting up a Great Firewall and banning anyone from running a public web or email server without a license. (Justified by preventing phishing, preventing spam, protecting the children, monitoring terrorist communication, etc.)

In Australia the government has already shown their willingness to set up a blacklist of blocked sites (although that proposal doesn't look like being implemented any time soon).