Did a bit of research. There was a Bugs Bunny cartoon, back in the days when they played before popular movies, where Bugs is engaging in his favorite hobby, tormenting Elmer Fudd in rabbit-hunting mode (shotgun and stupid floppy hat).
Bugs is about to do something awful to Elmer, and then says, "Neh, I couldn't do that to the little nimrod."
It then got picked up as a popular synonym for a dumbbell*
The WAV file of the line can be found here.
If true, this is fascinating, since although I knew Nimrod was an Old Testament character, I had not known that it was a synonym for "hunter," which implies that the folks who made Bugs Bunny cartoons were a lot more educated than many people would suspect. But then, anyone watching the old Chuck Jones cartoons KNEW that.
*where did THAT one come from?
Current Events » in reply to short changed ol' Nimrod
The origin of "Nimrod"