In the interests of national security and protecting the safety and security of the American public the federal government should have the ability restrict or "kill" public access to the Internet. The fact that the Internet is now a tool used by terrorists and other enemies of the United States the ability to control Internet access in the event of national emergency is needed by the federal government.
No, the U.S. government should not be able to shut down the internet during a national emergency, because that is when the internet is most important. People would need to communicate with each other about threats, and also about evacuation and safety planning. Many Americans do not trust their own government, and worry that the U.S. government would only try to shut down the internet in order to control information.
The Internet has been responsible for allowing people to organize quickly. When people need to raise funds, often they are able to do it because of the Internet. The Internet also allows people to exchange information about political ideas. It also lets people talk to family and friends. Governments shouldn't just be able to end it for no reason.
On the whole most governments want to expand internet access. However governments do not seem to have taken into account the potential repercussions of the shutdowns, beyond the limits of free speech. Many of them see it as an opportunity to participate in the global economy and be competitive. That there were many ways that internet access can be limited, beyond state-sanctioned shutdowns.