As the title suggests, I am curious where the term came from. A twenty-minute Google search did not yield any useful results.
More specifically, I am wondering why the word "cheap" was used.
Etymonline says about cheap and cheap shot that
Sense of "lightly esteemed, common" is from 1590s....
Cheap shot originally was U.S. football jargon for a head-on tackle; extended sense "unfair hit" in politics, etc. is by 1970.
But in Esquire, 1966, the etymology at Etymonline is contradicted by a letter-writer:
Professional football players do not now, and probably never did, refer to a head-on tackle as a "cheap shot." A head-on tackle is not won cheaply.
So the sense given by Etymonline for both cheap and cheap shot doesn't seem to be correct.
