What is the nickname of the only u. s. president born on the 4th of july?

The only U.S. President born on th 4th of July, Calvin Coolidge, was nicknamed "Silent Cal".

Explanation:

Although Coolidge was a good speaker, in private he was a man of few words, so he drew the nickname. An anecdote, perhaps apocryphal, but which perfectly defined the impression that Coolidge produced: a midwife, sitting next to him at a dinner, said "Today I bet I would get more than two words out of it"; Coolidge replied: “He has lost.”

Coolidge's fame of laconism lasted during his term as president. He later declared: "The words of a president have great influence and should not be pronounced in vain." He was aware of his image of adulthood which, in fact, he encouraged. Some historians later affirmed that Coolidge's image was actually an electoral tactic, while others believed that their withdrawal and silence were natural and that they worsened after the death of their youngest son in 1924.