Actually, without Jesus, Judaism is incomplete. The Old Testament, even as far back as Genesis 3, speaks of a Deliverer, a Messiah, a Savior. This Deliverer would come through the line of Abraham and be the blessing to all people that God promised Abraham.
I want to point out that I am distinguishing Biblical Judaism from rabbinical Judaism. I'm defining Biblical Judaism as acknowledging Jesus as the fulfillment of the Biblical prophecies. Messianic Jews fit this definition of Biblical Judaism. Rabbinical Judaism denies Jesus, of course, but still has no Messiah that has yet come. Still culture and traditions are followed.
The Scriptures foretold when and where the Messiah would be born, that He would be called "God with us", that He would die and rise again, that He would be rejected by His people, and on and on. So, without Jesus, Judaism is incomplete, with God being silent and ignoring the Jewish people for 2500 years. Furthermore, within a generation of the Jewish leaders rejection of Jesus as the Messiah, the Jewish nation was conquered and the Temple destroyed. This lasted for nearly 1900 years. (This dispersion and regathering was also prophesied.)
The apostles never saw themselves as anything other than Jewish. Indeed, the most Jewish thing a Jewish person can do is recognize the Jewish Messiah. Jesus fulfilled the promise to be a Deliverer not only for the people of Israel, but for the whole world. (Isaiah 49:6 and others)
Without Jesus, Judaism is without a Messiah. Without Jesus, Judaism has not been a blessing to all people. Without Jesus, the Jewish prophecies remain unfulfilled and must be considered false.
So, Jesus' teachings fit completely within Judaism, and true Judaism recognizes Jesus as the Jewish Messiah prophesied in the Jewish Scriptures.