I. First Amendment Issues
Threats are not protected speech under the First Amendment and thus may be criminally punished. In determining whether a communication is a "true threat" (not protected) as opposed to a joke/euphamism/political hyperbole, the federal courts use a two-part test. First, they ask if a reasonable person in the threatener's position would have expected the recipient of the communication to perceive the communication as a threat. (Some circuits ask if a reasonable recipient would have perceived the communication as a threat, but there is no noticeable difference between the outcome of the two tests.) Second, they ask if the threat was sufficiently unequivocal, unconditional, immediate, etc. as to convey a gravity of purpose (imminent prospect of death OR violence against the recipeint) to the recipient. In analyzing these two factors the circumstances surrounding the communication are heavily considered.
Example: In Watts v. United States, 394 U.S. 705 (1969), the Supreme Court said that the statement "If they ever make me carry a rifle the first man I want to get in my sights is L.B.J." was constitutionally protected "political hyperbole" and not a threat because the statement was made at a political rally, the listeners laughed in response, and the young man had already said that he would never carry a rifle.)
II. Criminal Punishment
Not all constitutionally unprotected threats are punished. Federally, 18 U.S.C. §871 makes it illegal to threaten the president. However, state penal codes preventing threats against private citizens vary state to state, and often use a narrower test than the one outlined above.
Example: Cal. Pen. Code §422 punishes threats only if the threatener intended the communication to be taken as a threat and the recipient suffered sustained, reasonable fear as a result of the threat. Thus, if the threatener did not intend to intimidate the recipient (although a reasonable person would have felt threatened) or the recipient did not personally suffer fear as a result of the threat, the threat will not be punished under California law. However, if the same statement was to be uttered in reference to the President, the threatener would be guilty under 18 U.S.C. §871.
That'll be $600, please.