I have learned that Craftsman tap and die sets are what's call rethreading sets. The are high carbon steel, not HSS, and it makes a big difference as they last much longer and cut soft-semihard steel, unlike the high carbons which dull very quickly, and is most likely the source of your problem. I have used the same technique of chucking the tap in the tail stock. It generally works great. If the dies are all hex in the set, this is a indication that they are high carbon. HSS will be clearly marked on them if they are.
SteveK