As a student of the history of the use of "the Judeo-Christian tradition" in American public discourse, I can't resist posting this Blitzer-mediated exchange between Carville and Donatelli on the president's remarks concerning the kind of nation the United States is: not Christian or Jewish or Muslim but "a nation of citizens." That is, of course, exactly what the founders had in mind, and Obama is obliquely referring here to Washington's famous 1790 letter to the Jews of Newport that makes that point:
It is now no more that toleration is spoken of as if it were the indulgence of one class of people that another enjoyed the exercise of their inherent natural rights, for, happily, the Government of the United States, which gives to bigotry no sanction, to persecution no assistance, requires only that they who live under its protection should demean themselves as good citizens in giving it on all occasions their effectual support.
Donatelli thinks such statements should not be made, as if in doing so the religious heritage of the country is dismissed or demeaned. Not that the founders would have identified that heritage as "Judeo-Christian." That shibboleth dates to World War II (Wikipedia doesn't have it quite right), and really only came into its own during the Cold War. Dwight Eisenhower used it in his notorious (misquoted) statement implying that America needed religion but that it didn't matter what kind of religion. (For a complete discussion, see my 1984 American Quarterly article, "Notes on the Judeo-Christian Tradition in America.")
What the Washington-Obama position is based on, however, is not a belief in the necessity of some kind religious underpinning for the American approach to religion, unless by that is meant a belief that the Judeo-Christian tradition is particularly given to recognizing humankind's "inherent natural rights," and in particular a right of conscience. That's a debatable proposition.
I've not done any research but I've always suspected that the phrase "Judeo-Christian" came into use once Jews and Christians faced the threat of godless communists ("the enemy of my enemy is my friend" and all that). Do you recommend any resources on that topic other than the American Quarterly article you cite above?
Actually, it came into use during World War II as an anti-fascist term. "Christian" was a word often adopted by fascist organizations and publications, and Judeo-Christian served to include Jews under a common spiritual umbrella. The Wikipedia entry on the term has some additional bibliography.