> Can the government compel my speech ? Can the government compel me to make false statements ?
These are interesting questions, but I'm not at all sure the answer is not 'yes' to both of them, under the right circumstances.
The Fifth Amendment would not seem to imply (there's no criminal proceeding, and not necessarily any risk of self-incrimination) and the First Amendment, while applicable, would not necessarily prevent such a thing, in my estimation, if the circumstances were (in the government's estimation) sufficiently dire.
Alternatively, in some cases the USG could simply seize the domain name and/or server and serve up any content they wanted. See, e.g., Playpen. http://arstechnica.com/tech-policy/2016/01/after-fbi-briefly... Though presumably they could not do this if the site or service operator were not also implicated in some form of illegal activity.