John Adams may have been obnoxious and disliked but he was right there in the thick of the Declaration of Independence. According to this article, he thought we should have celebrated American independence on the Second of July.
I suppose it's too late to change now. For one thing, it would screw up some song lyrics and movie titles. But it is interesting to know. Thanks to James J. Troutman for letting me know so I could let you know.