People often use Christian for Judeo-Christian.
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Only if they are Christian. Can you honestly say that you have heard a Jewish person do so?
I would expect a Jew to emphasize Jewish law; when Katherine Harris is discussing a choice between herself (a Christian) and Bill Nelson (remember, her answer was in the context of Q: Why should Florida Baptists care about this primary election? A: They should care about this election period...."), I would expect her to say Christian, since, in this election, she is supporting electing herself, a Christian. What's she going to say, elect a godly Jew for Florida Senate 2006? That's more than a little silly.
(Although if there were a godly Jew in the race I'd be supporting him over Harris, so maybe that's not that far-fetched! As it is, I'm supporting McBride in the primary. Harris is toast.)