What does Luke 13:33 mean?

Jesus is talking to Pharisees who have warned Him to flee because Herod Antipas wants to kill Him (Luke 13:31–32). This is not a good-faith warning. More likely, it is some combination of taunting and a threat. Again, Jesus uses a curious phrase referencing three days: today, tomorrow, and the next day. In the previous verse, Jesus used it to describe when He would complete His work. Now He uses it to say when He will complete His journey to the place where His work will be completed.

This is clearly a figure of speech, but in this exact application, scholars aren't sure what Jesus means, other than a short amount of time. It may obliquely refer to the three days He was in the grave and rose on the third day. It doesn't literally mean the time from this encounter until Jesus enters Jerusalem.

The Old Testament carries a pattern with time and threes. In many places, three days is the period during which a matter is decided, the resolution coming upon the third day (Genesis 40:12–13, 18:19; Exodus 15:22–24; Ezra 8:15, 32; 10:8; Nehemiah 2:11). If Jesus' words echo that idea, He is saying that He has a set amount of time in which to work before a resolution takes place: His entrance into Jerusalem. He isn't worried about Antipas; He has not yet finished His Father's business of "[casting] out demons and [performing] cures" (Luke 13:32), so His life is safe. On the symbolic third day, Antipas will have his chance (Luke 23:6–12).

Jesus' comment about the perishing prophets, however, doesn't refer to Antipas but to the Pharisees. Not long ago, He told a room full of Pharisees and their lawyers what He thought of their piety. They follow the laws that made them look good but neglect those that show love or promote truth. Of the lawyers, otherwise known as scribes, He said that because they hide the truth that the prophets spoke about, they are as guilty as their forebears who murdered those prophets (Luke 11:47–52). Like Jerusalem itself, they are worthy of judgment (Luke 13:34).

Jesus does die in Jerusalem, but not all the Old Testament prophets did. Metaphorically, however, many were killed by the Jewish religious leadership that was based in Jerusalem.