In the case of Chaplinsky v. New Hampshire, the Supreme Court recognized a First Amendment exception for "fighting words", which it described as "those which by their very utterance [1] inflict injury or [2] tend to incite an immediate breach of the peace." In the decades since this 1940 decision, the Court has limited its effects to the most challenging and confrontational of words spoken in a face to face encounter and likely to lead to immediate fighting.
In Brandenburg v. Ohio, the Court held that an apparent threat uttered at a KKK rally--if the government keeps cracking down on white people, "there will have to be some revengence taken"-- did not give a prospect of immediate action and was therefore First Amendment protected.