No. A 'jew' is what the Pharisees became, the people who followed 'the traditions of the rabbis'. The 'rabbis' are teachers or 'learned' men, they are not priests, they are not a race. The references to Jesus as a 'rabbi' signify he was well versed in Scripture and taught/corrected other people in regards to it. The traditions of the rabbis, or the traditions of 'men' in other words, mean that the jews regard the ideas and writings of humans above those of God (as told by His prophets and in Scripture). This was a big part of what Jesus criticised, telling the pharisees that they were wrong for equating their traditions with those of God, among many other things.
Judea was a geographical area. Judah was a son of Israel (who was Jacob), and is thus what one of the tribes of Israel was called. The area is named after Judah because they were the largest of the surviving tribes, the others being lost among the rest of the world or dead after God destroyed them for their crimes.
Israel is the son of Isaac, who was called Jacob before his meeting with God. The Israelites are from the 12 tribes of Israel, the tribes being named after his sons.
The Hebrews were the sons of Ever, of whom Abraham (and consequently Israel/Jacob) is a descendant. Abraham and Isaac are thus Hebrews and not Israelites, whilst Judah is an Israelite.
Jesus was from the tribe of Judah. King David was of the tribe of Judah, and King David is one of Jesus' ancestors according to the New Testament, and as is necessitated by prophecy.
Being a 'Judean' (of the tribe of Judah) thus does not make him a 'jew'. Judaism did not even exist in Jesus' time, their predecessors the Pharisees (who followed thetraditions of men as opposed to God) would later become the jews (and their traditions of men would be codified in the talmud).
The Pharisees are one of the main antagonists in the Gospels, and Jesus is frequently seen arguing with them, even going so far as to call them 'a brood of vipers', 'of their father the devil' and 'of the synagogue of satan'.
The idea that Jesus could be a jew is preposterous and comes only from ignorant people who do not understand the meanings and differences in the words which I have explained above.