If the Internet shuts down, Bitcoin will die. At least, temporarily. It's possible that nodes would connect to a mesh network or something, resulting in the "revival" of the Blockchain. But at that point, Bitcoin will be so weak, it would be easy enough to attack it. After all, not all nodes are miners. What if most miners don't find a way to connect to the same mesh network as the nodes? Satellites could work, but signal fidelity would greatly depend on weather conditions. In essence, Bitcoin would be "weakened" to a point where no one will care about using it.

I doubt governments will act in unison and shut down the whole Internet. Not only it's impossible, but it would also disrupt online businesses and services. It would be complete chaos. Definitely not worth the effort. Fingers crossed an individual or corporation runs Bitcoin nodes in space to avoid this kind of situation. One can only hope...