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"Do me a favor" means "no", with an attitude. Similar in meaning to the outdated phrase, "talk to the hand". When one person asks another person to do something undesirable, the response may be, "do me a favor". No specific favor is given, but the recipient is free to imagine one (go jump in the lake, etc.).
Wife: "Honey, can you take out the trash?"

Husband: "Do me a favor."
by Buck33wheat September 03, 2009