An Elephind search turns up a number of relatively mild yet colorful antecedents to the more vulgar "couldn't organize an X in a Y" expressions that Andrew Grimm mentions.
From "The Banana Busisiness," in the [Washington, D.C.] Evening Times (April 15, 1899), reprinted from the New Orleans [Louisiana] Times-Democrat:
Why, the Chinese banana growers of Bocas couldn't organize a flatboat.
From an untitled item in the [McConnellsburg, Pennsylvania] Fulton County News (June 21, 1905), reprinted over the ensuing month in newspapers in Virginia and Washington State:
Men who couldn't organize a peanut stand know just how the pastor should run the church.
From Frank Crane, "Recognize Mexico," in the [Roanoke, Virginia] World News (June 8, 1922):
About the time of de la Huerta's visit, a revolution was staged under the leadership of Felix Diaz. Diaz is a toothless has-been, and couldn't organize a revolution in a chicken coop.
From Lemuel Parton, "Dollars Will Go Swiftly During Approaching Political Campaign Despite Huge Sums to Be Raised," in the San Bernardino [California] Sun (July 25, 1928):
Some of them are experienced political workers who know how to organize a district; others are out-moded and broken-down politicians who couldn't organize a game of horseshoes and still others are confidence men who are accustomed to selling political prestige which they do not possess.
Expressions that appear in newspapers from the 1970s and later include the following:
couldn’t organize a two-car funeral Golden [Colorado] Transcript (April 7, 1972)
couldn't organize a box lunch [Denver, Colorado] Paper (August 2, 1972)
couldn’t organize a procession to the bathroom [Denver Colorado] Fourth Estate (April 10, 1974)
couldn’t organize a one-car funeral Santa Cruz [California] Sentinel (May 7, 1981)
couldn't organize a rock to fall off a cliff Canadian [Texas] Record (August 1, 2002)
couldn't organize a bake sale Coronado [California] Eagle and Journal (December 3, 2008)
Google Books search delivers a number of additional possibilities, going back to 1915:
couldn't organize a clambake Trumbull Electric Manufacturing Co., Trumbull Cheer (1915)
couldn't organize a bunch of tom-cats around a bowl of milk International Woodworkers of America, Proceedings of the Constitutional Convention (1939)
couldn't organize a game of slapjack Paul Bonner, Excelsior (1955)
couldn't organize a crap game William Brammer, The Gay Place (1961)
I have encountered the "game of horseshoes," "bake sale," and "one-car [or two-car] funeral" variants of organizational haplessness over the years; but for fidelity to the form that Andrew Grimm is most interested in, "couldn't organize a revolution in a chicken coop" is pretty hard to beat.