I think Tom Paxton wrote the "Draft Dodger Rag" --

I'm just a typical American boy
From a typical American town
I believe in God and Senator Dodd
And keepin' ol' Castro down.
And when it came my time to serve
I knew better dead than Red,
But when I got to my old draft board
Buddy this is what I said,

"Sarge I'm only eighteen
I got a ruptured spleen
And I always carry a purse.
I got eyes like a bat
And my feet are flat
And my asthma's gettin' worse.
Consider my career
My sweetheart dear
And my poor old invalid aunt,
Besides I ain't no fool
I'm a-goin' to school
And I'm workin' in a defense plant."