Michael Sean Winters of the National Catholic Reporter writes about the founders and the attempts by the Catholic bishops to Catholicize the founding in their fortnight for freedom. You can read MSW's excellent piece, which mainly focuses on Washington and whether he took Eucharist, can be found at http://ncronline.org/blogs/distinctly-catholic/happy-july-4th-was-americ.... I hit a few big topics MSW missed or soft pedaled.
Let's start with one thing first. Religious freedom, essentially the freedom of groups to exit other sects, especially state sponsored ones (and Catholic ones) was the essence of the original settlement and is reflected in the founding. However, the right to religious freedom started in the US with the Bill of Rights - which while a founding movement has nothing to do with July 4th.
There is one more factor in the American founding that bears mention and that evicerates the Church's attempts to Catholicize the founding. It is fairly obvious if you ever go to the King Street Metro station. It is Free Masonry. Whatever he did on Sunday, George Washington was a Mason. Indeed, everyone who was anyone was a lodge member. In my own mother's family, who were part of the first generation, participation in the lodge or White Shrine carried down to at least my mother, who was a rainbow girl and only left the movement to convert to Catholicism and marry my father. I know my grandfather was a Mason and if my mother was a Rainbow Girl, I suspect that her half brother, my uncle Kermit, was a Mason - although because of divorce he might not have been initiated. (any wonder why I don't join this odd commemoratio by the bishops?)
While the enlightenment (some may say illuminated) ideas of the Masons were part of the founding, it was not some ruling cabal. It was an is a civic and fraternal organization, like the Knights of Columbus. Indeed, the reason for the nights to exist at all was Catholic fear of masonic ideals. Despite the pseudo-Americanist language in the Fortnight for Freedom, their claim does not hold water - you cannnt catholicize something you condemn. What has changed is that I suspect Catholic are joining anyway and not bothering to mention it in confession (in prior years, the distrust was mutual and Catholics could not be inititated anyway) and there is now an unholy alliance in the pro-life movement between Catholics and Evangelicals - and the Evangelicals love that Americanist language - although they were not that much part of the founding either, with many having not yet immigrated to where they are today. Indeed, neither had that Catholics.