It's unlikely or perhaps even impossible that it originated as a reference to President Lyndon Johson, because Websters cites its first recorded usage back to 1863. Maybe its an offshoot of the British slang "John Thomas" which was slang for penis.More than likely it's because as President, Johnson was known to be an avid skinney dipper.
AnswerI'm not sure what Johnson did in 1960, but in 1964, having assumed the presidency after the Kennedy assassination in 1963, he launched a program called the Great Society. The following link will take you to a 1964 graduation speech he made in Michigan in which he talks about the Great Society. http://coursesa.matrix.msu.edu/~hst306/documents/great.html
Lyndon Baines Johnson (LBJ)
Great Society
Johnson had initiatives to provide insurance and health care for the elderly and poor, to improve education and housing for the poor, to encourage and expand the arts and educational television, and to protect and repair damage to the environment.
Lyndon Johnson graduated from Texas State University when it was called Southwest Texas State.
"Johnson" is slang for the penis.
a "Johnson" is a slang term for a penis!! as in "don't let your Johnson get caught in your fly"
The large veins on the penis are called the dorsal veins of the penis.
very big and hot
Penis
It is called a penis.
There is no alternate term for a horse's penis.
The baculum (also called the penis bone, penile bone or os penis) is a bone found in the penis of many placental mammals including raccoons.
It is not possible to flatulate out of your penis. Air should not be coming out of your penis.
Because the hair was in the shape of a penis, aka "johnson".
Penis
It is called the penis. Or in Latin, the phallus.