It has only been in the last eight or ten years, as far as I can tell, that scholars as a collective voice have been reacting to this problem in their publications on the historical Jesus, demanding that we take seriously the obvious - that Jesus was Jewish. Jesus as a Jew is not just another agenda-driven "construct" as some have been suggesting (this really is a hyper-post-Modern stance). Being Jewish was Jesus' self-identity, and it has taken us two thousand years to admit it and talk about what it means. No amount of pressing the button on the "diversity" and/or Hellenization of early Judaism is going to erase the fact that for Jesus the Torah and prophets were his scriptures, the Temple his cult, Yahweh his god, and the coming of God's Kingdom his hope. Jesus as Jewish is probably the most essential (and dangerous) idea that I can think of.
Susannah Heschel has written a fascinating book on Abraham Geiger, who already in the 19th century constructed a Jewish Jesus, seeing him as a Pharisee who came to reform Judaism. He also denounced the anti-Judaism of Christian scholars of Judaism. It is interesting that Geiger's arguments (and those by other Jewish scholars of Jesus) are finally getting their just due.