I don't think anyone knows whether the entire Internet could be shut down. It has never happened, so there is zero empirical data to build an expectation. Obviously, the decentralized nature of the Internet makes it nearly impossible to shut it down 100%. Perhaps we'll get to test this empirically in a few years when the predicted increase in Solar storms fries a big portion the World's electronics.

However, I'd bet dollars to donuts that there exists a highly classified plan to shutdown the majority of the Internet if truly necessary for an extraordinary emergency. The DoD make plans for everything they might need to handle and they get $500+ billion a year carte blanche. If you had 100 cruise missiles, a dozen nuclear subs, thousands of special forces teams and around 50 spy satellites, how hard would it be to shatter the Internet into countless disconnected networks?

This is a fun and practical math problem in optimization and graph theory: What's the minimal number of cut undersea cables, missiled satellites, bombed microwave stations, and blown up peer exchanges and telecom backbone data centers to cause the maximal number of disconnected networks?

What if the exact answer is 42?

(I won't say "42 of what?", since it could refer to any number of things, but what if 99% of the Internet could be reduced to a finite list of attack targets, given the logistical ability to attack them?)

Does the US gov't have the resources to pull off these kind of logistics in a true WTSHTF emergency?

Yes, I think so.

At the very least, they need to know how to stop any potential enemies from shutting down the Internet, so in order to know how to protect it they also need to know how to destroy it.