When Christians say this "they're waiting for their Messiah" I get the feeling that Christians think that Jews are looking for someone to do pretty much the same thing Christians claim Jesus does for us.
Evangelical Christians often use the expression "He paid the penalty for our sins" to describe what Jesus does for us. Amongst Jews, there is debate as to whether they are even looking for an individual Messiah, (as opposed to a Messianic Age), and if they are, I seriously doubt that they are looking for a Messiah to pay the penalty for our sins and replace the Jewish sacrificial system. I'm not saying that that kind of Suffering Servant isn't foreshadowed in the Hebrew Scriptures, but I do think that Christians and Jews have different Messiah-concepts. Just because they use the same word doesn't mean they have the same things in mind.
I am supplying a link to the Wikipedia entry on the Messianic Age.