What does Luke 11:17 mean?

Jesus has healed a blind and mute man whose conditions were caused by demon possession (Luke 11:14; Matthew 12:22). Visiting scribes, experts in the Mosaic law and the extra-biblical Oral Law, have come down from Jerusalem to witness Jesus' ministry first-hand. After seeing this incredible miracle, they have decided that Jesus cast out the demon by the power of Satan. Jesus is in the process of explaining why this is ridiculous (Luke 11:15–16).

It's very possible that by talking about divided kingdoms Jesus is alluding to—and the people are reminded of—what happened when Solomon's son Rehoboam took the throne. Rehoboam put such a burden on the people that his rival, Jeroboam, had no trouble taking ten tribes from the nation of Israel. This divided the northern kingdom of Israel from the southern kingdom of Judah (1 Kings 12:16–20). The nation was recovered for a short time under the Maccabees, but at Jesus' time the land is divided into Galilee, Samaria, and Judea under the authority of the Roman Empire.

The illustration of the divided family is exemplified by the Herodians. At Jesus' birth, Herod the Great ruled Idumea, Judea, Samaria, Galilee, Decapolis, Perea, and districts to the north. When he died, his territory was split, three of his sons taking smaller territories. Not long after, the largest region was placed under a Roman procurator.

So, in Jesus' era, Jews were constantly reminded of what a divided kingdom and family look like. Jewish autonomy was definitively "laid waste."

This is not the first time Jesus has known the thoughts of His adversaries (Luke 5:22; 6:8; 7:39–40). He knows both that the religious leaders from Jerusalem are intentionally being obtuse about His relationship to God and that more others haven't made up their minds and want to see more miracles (Luke 11:15–16).