Well, if Jesus claimed to be the Messiah, that would count as proclaiming himself King of the Jews. The Messiah's of the line of David, meant to restore Israel and rule as the king.
While I don't remember reading that Jesus ever came out and said, specifically "Hey, guys! Messiah over here!" He does strongly imply that he's fulfilling a bunch of prophecies in his message to John the Baptist in Luke 7:22. It seems to me that his response is meant to make John the Baptist believe that Jesus is most definitely the Messiah.
That's why the Romans thought their taunts were so effective. It was generally understood that Jesus was proclaiming for himself a leadership role, but had been utterly rejected by most of his people. Imagine (Americans) calling McCain "Mr. President" the day after he lost the election.