What does Luke 11:20 mean?

Religious leaders from Jerusalem (Mark 3:22) claim Jesus casts out demons by the power of Satan. Jesus has given two reasons why they can't make this argument. First, if Satan ordered a servant to cast out another servant, his kingdom would fall (Luke 11:17–18). Second, if the sons of the scribes and Pharisees cast out demons by the power of God, then how can Jesus do so by the power of Satan (Luke 11:19)?

Here, Jesus comes to His deeper point. He has healed a man who was blind and mute (Matthew 12:22; Luke 11:14). No one else in the Bible is recorded as healing the blind and the mute, but the prophecies do promise the Messiah will do so (Isaiah 35:5–6). If Jesus casts out demons by God's power and provides healing only the Messiah can, then He is the manifestation of the kingdom of God. If He is the manifestation of the kingdom of God, why don't they listen to Him? Why don't these experts in the Jewish Scriptures recognize who He is? They have no excuse.

Here, as in other passages, interpreters differ on the nuances implied in Luke's phrasing, specifically as related to the "kingdom of God." The phrase gives scholars and theologians many opportunities to display their academic prowess (Ecclesiastes 12:12). Scholars who see the "kingdom of God" as something that is both "now and not yet" simply say that when Jesus arrived His kingdom was inaugurated and remains in His church. At His second coming it will be fulfilled (Acts 3:19–24).

Where Luke talks about the "finger" of God, Matthew uses the "Spirit" of God and, after the parable of the strong man, discusses blasphemy against the Holy Spirit (Matthew 12:28–32). God's finger as a sign of His power is found in several places in the Mosaic writings (Exodus 31:18; Deuteronomy 9:10; Psalm 8:3). The lawyers should recognize it.