John Wilkes Booth broke his leg while escaping after shooting Abraham Lincoln. He was given medical help by Dr Samuel Mudd, who didn't then know about the assassination. Mudd was wrongly convicted of being Booth's conspirator. Actually the phrase was in wide circulation before Mudd was defamed. Mudd was born in 1830: this comes from an 1823 slang dictionary, "'And his name is mud!' Ejaculated upon the conclusion of a silly oration, or of a leader in the Courier." The phrase appears to be one of the many that, when a news story arises, match the jist of the story and later become associated with it.(Source)