he was only off by two days

So he got the date wrong. Give him a break. He's John Adams, for crying out loud.

He wrote the following in a letter to his wife Abigail, on July 3, 1776:

The second day of July, 1776, will be memorable epocha 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, shews, games, sports, guns, bells, bonfires and illuminations, from one end of the continent to the other, from this time forward forever.

Happy birthday, America. And, happy birthday to me, too.