I'd imagine this'll go the same way as Murdoch's had it in the UK, with most politicians simply too scared to go up against them, because they have some kind of skeleton in the closet that will be making a loud public appearance the moment they try to fight the bad guy. (Newspapers/Anon).
It's only because News International have gone so far and offended so much of the British public that the politicians have had their hands forced into looking like they're doing something.
I'm not sure how far Anon would have to go, but I believe if and when the US government decide to take them on, it'll both be a disaster because I imagine they'll just attack anyone vaguely related, like lists of people who've watched an Anon video on youtube, such has been proved of the quality of their 'online intelligence'.
It'll be like throwing grenades thru a whole street's front windows to get rid of some rats, there's gonna be huge collateral damage, the solution will look really stupid and expensive and the rats were in another town anyway.
As much as Anon and others like them have caused costs to corporations and embarrassed governments, I'm kinda on their side until they do some real damage that isn't exposing idiocy.
EDIT: IF you're out there, Anon, please, please, do something awful to the new News Inc 'Sun on Sunday' site for their relaunch of the News of the World under a new name.
Just a spoofed front page with the headline 'Immigrants, gays and muslims 'fine' say experts' or something like that