http://www4.law.cornell.edu/uscode/18/875.html

To constitute "a communication containing a threat" under Section 875(c), a communication must be such that a reasonable person (1) would take the statement as a serious expression of an intention to inflict bodily harm (the mens rea), and (2) would perceive such expression as being communicated to effect some change or achieve some goal through intimidation (the actus reus). A message is a "threat" if a reasonable recipient would tend to believe that the originator of the message was serious about his words and intended to effect the violence or other harm forewarned, regardless of the speaker's actual motive for issuing the communication.

Any person who willfully threatens to commit a crime which will result in death or great bodily injury to another person with the specific intent that the statement made verbally in writing or by means of an electronic communication device is to be taken as a threat even if there is no intent of actually carrying it out which on its face and under the circumstances in which it is made is so unequivocal unconditional immediate and specific as to convey to the person threatened a gravity of purpose and an immediate prospect of execution of the threat and thereby causes that person reasonably to be in sustained fear for his or her own safety or for his or her immediate family's safety.

It is not necessary for the victim to actually be placed in fear of imminent serious bodily injury or for the accused to have the capability or the intention to actually carry out the threat. The offense is completed if the accused, by his threat, sought as a desired reaction, to place a person in fear of imminent serious bodily injury.