It's fun to approach the altar on the 4th, with everyone feeling all patriotic dressed in red, white, and blue, and say, "Today the Church celebrates the feast of St. Elizabeth of Portugal.", and then ignore the civil holiday in favor of the Church's sanctoral cycle. I do it once every few years to remind people that not every civil holiday needs to be "sanctified" in church. I mean, we already make the Sundays of Mothers' and Fathers' Day into near-Solemnities. Besides, what about the blatantly religious holidays, like Christmas and Easter, that secular society has, well, secularized? There's gotta be some payback for that, no?
So what do I do on Independence Day in the other years, when I'm not getting accused of being a Tory? Glad you asked...
Sometimes I give a homilette on the history of Roman Catholicism in the United States, trying my best to incorporate the early missionaries from Spain and France, the Calvert family (a.k.a. the Lords Baltimore) and the settlement of Maryland, the Carrolls and their relationship with Ben Franklin and how that led to John Carroll being named the Prefect Apostolic of the United States, the Sulpicians of France trying to find safe haven from the French revolution by coming to the United States which led to the first seminary and the possibility of training a native clergy, the arrival of Carmelites at Port Tobacco and the Visitation Sisters in Georgetown, all in 5 minutes.
Finally, sometimes I use this: A few years ago, I came across a great article about how Thomas Jefferson was influenced by the writings of Cardinal Robert Bellarmine (who got it from Aquinas), and how our Declaration of Independence has its roots in Catholic moral teaching. Yes, Jefferson saw Jesus Christ as simply a philosopher, and rewrote the bible to his own liking (taking out miracles and anything that made Jesus seem like God). But the article is great at showing just who saw those "truths as self-evident" before the gang in Independence Hall.
Oh yeah, and then there was that one time when I was fighting the flu and took Nyquil nighttime formula instead of the daytime stuff, and ended up doing this:
But that's another story.