We just finished celebrating the Independence of the USA.
I'm not sure July 4 is the correct day to celebrate the beginning of the United States of America. It should be July 2.
On July 2, the Continental Congress approved a resolution to become independent. http://en.wikipedia.org/wiki/Lee_Resolution. What they approved on July 4 was the text of the Declaration of Independence. So it seems the decision to become independent was adopted July 2nd, while July 4th was approving how we were going to communicate that decision.
John Adams had this to say in a letter to his wife on July 3rd:
"The second day of July, 1776, will be the most memorable epoch in the history of America. I am apt to believe that it will be celebrated by succeeding generations as the great anniversary festival. It ought to be commemorated as the day of deliverance, by solemn acts of devotion to God Almighty. It ought to be solemnized with pomp and parade, with shows, games, sports, guns, bells, bonfires, and illuminations, from one end of this continent to the other, from this time forward forever more."
The next letter he wrote to his wife was July 7 and he didn't have anything to say about the vote to adopt the Declaration of Independence on July 4.
But now maybe you have to be a real history trivia nut to really worry if Independence Day is celebrated on the right day or not.