Chanting at a meeting or rally is hardly a serious threat; instigating that chant, however, could be.  Calling for someone to kill a public figure is, particularly if the address of their office or home is included.

I have on occasion been tempted to wish harm on someone who has harmed others, but I restrain myself because I refuse to descend to that level.  I also realize that what I write on comment boards, FaceBook or Twitter is public and no different from standing in the busiest spot in the city and shouting it into a megaphone, or saying it into a microphone on a local radio or television show.  

Social media is a public forum and posting under an assumed name or a cute handle does not change that.  Thinking that using a fake name absolves one from responsibility for one's speech or protects one from the consequences, including prosecution for hate speech, is stupid.  Thinking that one's real identity could not be found is naive.