The story
Probably a humorous elaboration of wake up (“to become more aware of a real-life situation; to concentrate on the matter in hand”), alluding to the fact that coffee is often consumed at breakfast time after waking up in the morning. The term was popularized by the American writer Esther Pauline “Eppie” Lederer (1918–2002), who used the pen name Ann Landers, in the syndicated newspaper advice column Ask Ann Landers.
Etymology from Wiktionary, CC BY-SA 4.0.