I was looking for information about the phrase "Go for broke" and dutifully checked the archives here. The post by Smokey Stover quoted the authoritative OED as follows:
Posted by Smokey Stover on July 07, 2006
In Reply to: Go for broke posted by Valerie on July 06, 2006
: Please tell me what is the meaning of ''go for broke'' thank you.
The OED tells us, as is its custom, what this phrase means without explaining why.
"h. to go for broke: to make strenuous efforts; to go 'all out'. U.S. slang.
1951 Amer. Speech XXVI. 26 Go for broke means to bend every effort, to 'shoot the works'. 1963 Guardian 5 June 6 If he were to go for broke on behalf of the Negroes..the President would endanger the moral reform cause. 1968 Ibid. 19 Feb. 1/7 The enemy is 'going all out-..he is going for broke'."
I'm guessing that it could come from gambling, since going for broke means putting all your resources into one effort (like putting all your money on one card or one throw of the dice), the failure of which will leave you broke (without resources, bankrupt, penniless).
Doing a little further digging, I found this website that gives the history of the US Army's 442nd Infantry.
"Go For Broke" appears to have been the unit's motto, adopted in 1943. I don't know how authoritative it is, but the site attributes the phrase to Hawaiian gambling slang popular at the time.