Wiktionary says this of "screw the pooch":
The term was first documented in the early "Mercury" days of the US space program. It came there from a Yale graduate named John Rawlings who helped design the astronauts' space suits. The phrase is actually a bastardization of an earlier, more vulgar and direct term which was slang for doing something very much the wrong way, as in "you are fucking the dog!" At Yale a friend of Rawlings', the radio DJ Jack May (a.k.a. "Candied Yam Jackson") amended this term to "screwing the pooch" which was simultaneously less vulgar and more pleasing to the ear.
The unsourced part about Rawlings and May was added by an anonymous user in 2008.
Since then, this information has been repeated on numerous websites. While it's quite plausible that "screw the pooch" is a euphemization of "fuck the dog" (Green's Dict of Slang agrees), the rest of this seems a little dubious. Various sources suggest that there was indeed a Joseph L. "Jack" May who DJ'ed "The Candied Yam Jackson Show" on the Yale radio station WYBC when he was an undergrad from 1947 to 1951. And Rawlings is mentioned alongside May/Jackson in this article about the Chi Delta Theta literary society in the Feb. 7, 1950 Yale Daily News:
"The chorus of the gods at dinner," as the motto of Chi Delta Theta requires, was sung and played, soothing the more savage breasts, by David Chavchavadze, 1950, "Candied Yam" Jackson and Med Bennett, 1950, and John Rawlings, 1950.
Anyone have firmer evidence about the origins of the phrase?
(Question from Ben Zimmer via ADS-L.)