I don't give a Massachusetts... to me would be just another, almost absurd, way of saying "I don't give a ****". Some people like to insert whatever they can think of into the "I don't give a ..." pattern.
I once had a student whose family members each chose a word to use in an emphatic situation when others might use profanity. He chose "saxophone" for his word. Another example as a favorite of mine is, "What the fff--ront porch?"