If we consider David's history, it will appear probable that he had an eye to his son, Absalom, as this enemy. If we look at Christ, probably Judas was the foe here intended, with the Scribes and Pharisees.
Related Commentaries of Psalms 55:3
Psalms 55:3
3 Because of the voice of the enemy, because of the oppression of the wicked: for they cast iniquity upon me, and in wrath they hate me.