The Herod that Jesus was warned about here was Antipas (thus Jesus is probably in the region of Perea at this time). This was the Herod who had slain John the baptizer and was currently jealous of Jesus' influence. One might be tempted to assume that the Pharisees are just trying to scare Jesus into leaving the region because of their dislike for Him, but this is unlikely since Jesus asks them to deliver a message to Herod for Him. Herod has desired to see Jesus for quite some time (cf. Luke 9:9; 23:8), but it is doubtful that he was hoping to put Him to death. This would have been a bad political move on his part (cf. Matt. 14:5). Herod's desire is to get Jesus out of his territory, for he fears that Jesus could lead an uprising against him. Thus, he sent the Pharisees to "warn" the Lord under the guise of friendship (i.e., the Pharisees pretend like they are doing Jesus a favor).
Clearly, Jesus was not afraid of any earthly power. He had work to accomplish, and He would do so fearlessly. He responds by calling Herod a "fox" (i.e., a sly, crafty fellow). Jesus calls him this for his cunningness in sending these messenger. It is interesting to note that there are no other Bible examples of Jesus using this expression of contempt.
"I cast out demons and perform cures today and tomorrow, and the third day I shall be perfected" (Luke 13:32). Jesus wanted the Pharisees and Herod to know that He wasn't going to leave the region out of fear. He would leave when He had completed His work there. The mentioning of the days should not be interpreted literally but symbolically. Jesus' point is that it would be just a short period of time before He would complete His earthly work (i.e., finish it; cf. John 19:30). The mentioning of the "third day" could perhaps be a veiled reference to Jesus' resurrection.
"Nevertheless I must journey today, tomorrow, and the day following; for it cannot be that a prophet should perish outside of Jerusalem" (Luke 13:33). In spite of the fact that He would not be moved by fear, He would soon have to leave their region and return to Jerusalem, the "prophet-slaying city." Jesus sarcastically, yet truthfully, implied that surely a man of God wouldn't be put to death anywhere else! He wouldn't leave because of fear, but He would leave in order to fulfill His God-given work. However, in the meantime Herod did not need to worry for Jesus had no intentions of leading a physical rebellion against him. Jesus was looking ahead to His rapidly approaching end in Jerusalem.
Jesus declared in Luke 13:34,35 - "O Jerusalem, Jerusalem, the one who kills the prophets and stones those who are sent to her! How often I wanted to gather your children together, as a hen gathers her brood under her wings, but you were not willing! See! Your house is left to you desolate; and assuredly I say to you, you shall not see Me until the time comes when you say, 'Blessed is He who comes in the name of the LORD!'"
Jesus' repetition of "Jerusalem," as well as His words regarding a hen gathering her brood, clearly indicate His feelings of tender love for the people of that city who He knew would soon put Him to death. His desire had always been to protect and comfort them (as their spiritual Savior), but they would not accept Him in such a capacity.
Because they had rejected Him (and the Father; cf. John 15:23) they would ultimately be destroyed spiritually - "Your house is left to you desolate" (Luke 13:35). They would not see Jesus again in Jerusalem until His triumphal entry into the city (cf. Matt. 21:9).