I would get into how this won't work and the issues with trying to hit the 13 DNS servers.
However, I'll just let you read about the last real attack which shut down 9 of 13 servers.
http://www.sans.org/reading_room/whitepapers/dns/secure-root-dns-servers_991
Honestly, I'd actually be tickled if they did it. What better way for the governments to take full control of the internet? All they'd have to do is keep the servers down while claiming that the attack did more damage than was advertised. (And how would Anonymous claim otherwise?) In the meantime, while the root servers are down, it wouldn't be too hard to either add a few steps to the process to help provide tracking information for who goes to what site or have the servers "accidently forget" the links between the DNS name and the IP address for troublesome sites such as Wikileaks. So, when they start bringing the servers up one at a time (to make sure their new steps work), the governments of the world now have both an internet more to their liking and a patsy to bear the brunt of everyone's wrath.
Hell, thinking about it, most people don't even really know how the servers work. It could be claimed that the servers were damaged beyond repair by the cyber-attack but, fortunately, a number of corporations (such as Comcast or AT&T) have volunteered their servers to be the new DNS servers. Most people would be so grateful to have their internet back that they wouldn't even notice an odd loss of net neutrality.
Honestly, this would be kinda funny in a "wow, you just managed to sink your own cause in one stroke" way.