See " deader than Kelsey’s nuts". There it means a brand of high quality lug nuts used on early Fords.
In poker, the "nut hand" is the best possible hand given all the cards that are visible on the table. Supposedly that comes from an era when a farmer or tradesman playing poker would put the axle nuts of his wagon wheel on the table as a guarantee that either he would not run and flee in his wagon if he lost, or that he was betting the wagon on the hand.
So was that what General McAuliffe had in mind at the Battle of the Bulge?