This page lists the highlights of case law regarding prior restraint and the First Amendment. Two pertinent cases are New York Times Co. v. United States, where the court held that despite the potential harm of publishing the revealed information, the prior restraint doctrine was more important (the government cannot prohibit speech before it happens). Reno v. ACLU affirms that even if a publication might cause harm to a class of people, that (limited) harm does not justify universally prohibiting the speech.
There is no criminal penalty arising from the government censoring speech. A civil lawsuit – "section 1983" – is possible against an official who illegally attempts to suppress expression contra the First Amendment. The award might be just a dollar if the person so oppressed cannot prove actual damage. Technically, the sky is the limit, and it just depends on how outrageous the jury finds the government's action. If the government were to order suppression of opposition to its policies, we could easily be in the territory of world-record awards for violation of civil rights.