There’s a close link between the stress pattern of I could care less and the kind that appears in certain sarcastic or self-deprecatory phrases that are associated with the Yiddish heritage and (especially) New York Jewish speech. Perhaps the best known is I should be so lucky!, in which the real sense is often “I have no hope of being so lucky”, a closely similar stress pattern with the same sarcastic inversion of meaning. There’s no evidence to suggest that I could care less came directly from Yiddish, but the similarity is suggestive. There are other American expressions that have a similar sarcastic inversion of apparent sense, such as Tell me about it!, which usually means “Don’t tell me about it, because I know all about it already”. These may come from similar sources.