This is a phrase used when someone is confused and cannot decide between two choices. It is derived from the conundrum faced by a teenage male who lives in a house with one bathroom and a large family. When you live in a house with lots of people you can only masturbate in the privacy of the bathroom. You also have limited time because everyone has to use the same bathroom. Hence the dilemma, should I shit or jack off, which everyone told you would cause you to go blind.
The running back put such a move on the linebacker he did not know whether to shit or go blind!
A set of nonsensical choices that indicate a high degree of confusion about what to do next, in the sense that neither of them is even remotely realistic but the party concerned is so radically confused that he might consider them.
Jake is Mike's best friend.
When Mike saw the damage Jake had done to his car, he didn't know whether to shit or go blind.