The truth is it absolutely wasn't. It's true that various forms of Christianity (with more virulent anti-Semitism than any “Judeo” component) were broadly popular with the general population at the time of founding, the intellectual elite who were the thought leaders shaping our model of government were largely members of the Enlightenment faction that started the whole idea of anti-religious secular liberalism.
The nuclear family also played little role in America’s foundation, only becoming dominant in the US sometime early in the latter half of the 20th Century, quite late in US history.
Though both the nuclear family and “Judeo-Christian” values being essential to the foundation of the American nation is one of the (fact-free) defining myths of American social conservatism of the late-20th Century to the modern day.