It's a pet peeve of mine. The use of "Judeo-Christian" as if a Jewish ethos and a Christian ethos could be combined. As if any Jewish or Christian ethos were monolithic to begin with. Besides, usually when people say "Judeo-Christian," what they mean is "Christian." The "Judeo" part is usually added for political purposes.
The best counter to the Judeo-Christian myth that I've seen is by Steven Katz in his very hard to find book Jewish Ideas and Concepts: The Building Blocks of the Jewish Intellectual Tradition (and here). This is an excellent book and provides a concise chance for a Christian to get accurate info on the Jewish rabbinical tradition without the danger of Christian Zionists' poisoning the well.
Katz makes it clear when he says "the 'Judeo-Christian tradition' is . . . a 'myth,' and realistically speaking, from the Jewish side at least, there is little on which such a tradition could be built" (ix). Katz first refutes the myth by pointing out that viewing each religion as monotheistic is itself problematic -- particularly to Jews. While Christians view themselves as monotheists, any Jewish attempt to explain the Trinity as monotheism would require some theological gymnastics. Therefore, "it seems accurate to note that Jews and Christians cannot both be correct" (ix). So any Judeo-Christian tradition which attempts to be built on the monotheism of both religions runs into problems off the bat.
He goes on to point out that, while Jews and Christians share the Hebrew bible as canon, Christians read these books specifically through the lens of Christ's salvific power. The story of Creation is read with Jesus being present. Adam is a prototype for Christ, etc. The fallenness of humanity is also a requirement of Christianity if Christ's suffering is going to be needed to redeem us. There is nothing of this sort in Judaism. There may be the need for repairing the world, but humanity itself is not condemned to original sin in the same way as in Christianity. This anthropological difference also makes any attempt at a Judeo-Christian tradition difficult.
The Christian and Jewish concepts of "messiah" are also greatly different. As Katz says, "it is important to state that Judaism and Christianity can never reach any theological rapprochement over this crucial issue because the concepts of 'Messiah' and 'messianism' mean something different in the two religions" (xi). Later he states that "the clearest and most important example of this difference is found in the fact that the personal soteriological function which is at the very center of Christian messianism, i.e., 'Jesus died for our sins,' is totally absent from Jewish messianism, which accords the Messiah no role in the drama of personal salvation and judgement. This is a central refutation to the Christian Zionism so loudly proclaimed by preachers such as John Hagee.
Simply put, Judaism and Christianity share no tradition. Historically, the two have been at odds since Acts. There is no shared historical tradition. There is no shared liturgical tradition. There is a nominal shared tradition in secular philosophy and the arts. There is also a similar moral standard between the two. This gives rise to the "Judeo-Christian values" variant. While slightly more accurate, its reflection of the "Judeo-Christian tradition" myth still makes it fall a bit flat. The only thing truly shared between Judaism and Christianity is the Hebrew bible/Old Testament. But as mentioned above, both traditions read these books from a different perspective.
More important than anything else, this myth of a shared tradition -- especially a shared theological tradition -- can be extremely dangerous when found in the violence prone variant of Christianity manifest in Christian Zionism. As mentioned earlier, Hagee and his ilk being at the center of that apostasy. Simply put, there is not one single shred of Scriptural theology in Hagee's work. I don't care how many verses he puts up on the multi-thousand dollar LED screen behind him.