I believe I said Biblical Judaism (and if I did not I apologize), meaning the entire Torah Theocracy . . . including the death penalty (at least theoretically) for idolatry, animal sacrifices, and certainly no religious freedom as understood by post-Lockean people. They could not have had any respect for such a religion, and could only have regarded it as the prototype of the medieval Catholic "theocracy" that was their bane. Jefferson and Madison were (after all) deists who rejected all revealed religion, and that very much includes the claims of Judaism.
I believe I have read that Jefferson regarded the Biblical system as based on an oriental satrapy, but I could be confusing him with Mark Twain (another "admirer of the Jews" who hated the Jewish religion). Jefferson certainly said that he didn't care how many "gxds" his neighbor worshiped, which is far from the attitude taken by HaShem, the original "Jealous G-d."
John Adams did indeed admire the Jews for "civilizing" the nations of the world. How much of the Holy Torah he acknowledged as being of Divine origin I do not know.
At any rate, the United States of America was not founded on Jewish principals but rather the principals of the "enlightenment." And while the Jews of the time may have welcomed that development as preferable to the centuries of persecution that preceded it, the "enlightenment" philosophy was no friend of HaShem or the Torah, as the anti-Semitism of the enlightenment philosophers makes clear. Hebraic mortar cemented the bricks, not of "American democracy," but of the "New England 'theocracy'" that preceded it.