What a great question. It wasn't in Word Detective nor World Wide Words. However, I did find it in Phrase Finder, where it says that the origin is from a soldier who had lost his arms and legs and had to be conveyed in a wicker wheelchair. Does anyone know any more?
basket caseslang (orig. U.S.), (a) a person (esp. a soldier) who has lost all four limbs; (b) transf., one who is emotionally or mentally unable to cope; something that is no longer functional, esp. a country that is unable to pay its debts or to feed its people;
1919U.S. Official Bull. (U.S. Comm. on Public Information) 28 Mar. 1/1 The Surgeon General of the Army..denies..that there is any foundation for the stories that have been circulated..of the existence of ‘*basket cases’ in our hospitals. 1944Yank 12 May 17 Maj. Gen. Norman T. Kirk, Surgeon General, says there is nothing to rumors of so-called ‘basket cases’-- cases of men with both legs and both arms amputated. 1967Saturday Rev. (U.S.) 25 Mar. 30/3 Kwame Nkrumah should not be written off as a political basket case. 1972Observer 24 Sept. 36/6 The ‘hero’, a legless, armless, faceless 1914-18 basket-case. 1973Ibid. 15 Apr. 6/2 The real basket cases of European agriculture are the Italians and the Bavarians. 1978 S. BRILL Teamsters vi. 227 He was a basket case because of Spilotro. A totally broken man, crying and whimpering. 1978 M. PUZO Fools Die xxiv. 275 ‘Hunchbacks are not as good as anybody else?’ I asked... ‘No..nor are people with one eye, basket cases and..chickenshit guys.’ 1982Newsweek 11 Jan. 21/2 On a continent that is full of economic basket cases, the small, landlocked nation is virtually debt free.
