Did the Jews, prior to Jesus, expect the Messiah to be divine, i.e. God Himself? Everything I can find seems to indicate that they expected him to be divinely appointed, divinely empowered, with divine authority, with kingly authority and priestly authority but I don’t see that necessarily the same as God Himself. Two passages could result in that expectation perhaps: Psalm 110:1 and Isa 7:14.
I was wondering this because of the people’s response to Jesus, especially as He started to make clear His divine association with God the Father.
You ask a great question. It does not appear that the Jewish people anticipated a truly divine Messiah. Messiah means “anointed one” – and the Jewish people did see such people as being closely connected with God in some way (e.g. as a representative of God, empowered by His Spirit, etc.).
Over time, the Jewish concept of Messiah evolved to include a royal, prophetic, and priestly function. In the interstamental period, particularly in the Psalms of Solomon, Messiah is regarded as a warrior-prince who would throw off the yoke of Rome and establish a Jewish kingdom. This is probably why Jesus is sometimes reluctant to identify himself as the Messiah in the Gospels.
However, when one reads the OT Messianic texts (like Ps. 110; etc.) in light of NT teachings, it becomes clear that it is quite possible to understand the OT conception of Messiah as being both human and divine. It may not have been clear to the OT Jewish people, but it does become clear in light of NT revelation. Indeed, I think Jesus makes this very point about Ps. 110 in Matt. 22:41-46.
Hope this helps a bit.