James Dickson cites in his text studies that show spur length correlated to age. Lovett also states the same in "Wild Turkey Hunting and Management". He also uses the Gould's turkey as an example of genetics "selecting" against longer spurs. And he mentions soil characteristics having an effect on sour length due to the abrasion basically grinding the spurs down.
So right there you have Age, Genetics, and Environment. Because a spur is a bone, just like deer antlers, I think nutrition could play a hand in it as well. You need proper nutrition to enable growth. However, I think it only plays a small part in spur growth; otherwise, spurs would grow infinitely with the turkey.
Seeing as how you don't see any turkeys with 4" and 5" spurs, I think that's a pretty safe hypothesis.
But, I think Age, Genetics, Environment, and Nutrition play a role. Depends on the subspecies as to what order.