First off, I doubt it would be possible for one country to actually "shut off" the entire internet. There's just too many servers in too many places. I don't think it would even be feasible for a country the size of the US to take itself off of the internet for any length of time.
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- Could the US shut down the entire net for everyone everywhere? No, not without resorting to DDOS attacks and other nefarious schemes. They could make it difficult by taking themselves offline, but thats about the end of it.
In fact, in the case of the US, it will be very easy... DNS server are located in US... shutdown the DNS server and browser will not be able to translate a URL address in a IP address...
US gov is already working on a similar tool for stop piracy :
http://www.salon.com/technology/dan_gillmor/2010/09/28/worldwide_authority_for_american_copyright_cops
The main mechanism of the bill is to interfere with the Internet's domain name system (DNS), which translates names like "www.eff.org" or "www.nytimes.com" into the IP addresses that computers use to communicate.
A other article : http://www.foxnews.com/politics/2010/09/29/engineers-slam-internet-censorship-ahead-key-vote/
If something like this is created, it will not be very difficult to shutdown any site in the US... in fact, it can work world wide since US DNS server are the master server... unless that you begin to memorize IP... by example, addresses 192.0.32.10 IPV4 or 2620:0:2d0:200::10 IPV6 in place of www.example.com !!!
Seem that large scale internet censorship is something who can be made easily in US...
So Obama's "Kill switch" would be to pull the plug on the DNS servers. That would shut down the internet for not only the USA, but the world (with the exception of their country codes root domains).
Should the government have such authority? No. Government abuses everything it is allowed to do. If you cede that power to them, you have just lost another part of your rights, freedoms and liberties.
Soon of later, they will have the authority... at the time being, there is some scary bills proposed by political that almost nobody know about...