According to my grandfather who was a soldier in World War-II, the phrase became popularized from when soldiers/sailors/airmen/marines during the wartime would be drinking at a bar or dance hall while on leave, usually on a Saturday night. All the single guys would of course try to pick up women to get laid. The term "dog" has long been used as a derogatory term to call an ugly woman, and a nicer was to put that was to call her a "pooch". Besides, the phrase "screwed the pooch" has a rhyme to it. Anyway, the poor schmuck who got way too drunk for his own good and ended up going home with the ugliest girl at the dance hall after closing time and boinking her was said to have "screwed the pooch"... sometimes getting her pregnant in this one-night-stand and thus having to marry her. From this type of situation came the notion that "screwing the pooch" morphed into general meaning of messing up (anything) in a bad way, usually due to one's stupid actions.