The phrase sixty-four dollar question, $64 question, sixty-four thousand dollar question and variants denote a crucial question or issue.

It originated in the question posed at the climax of Take It or Leave It, a US radio quiz for a prize of sixty-four dollars. The following is from the radio programme published in the Democrat and Chronicle (Rochester, New York) of 6^th July 1941:

10:00 P.M.
                                                                               Take It Or Leave It
A half-hour of fun and laughs as contestants hope for success on the sixty-four dollar questions. Eversharp.

According to Vincent Terrace in Radio Program Openings and Closings, 1931-1972 (2003), the quiz show was first broadcast on CBS from 1940 to 1947, then on NBC from 1947 to 1950; this game, in which players attempted to double their money by answering questions of increasing difficulty, was sponsored by Eversharp, and the announcer opened the show by saying:

Eversharp presents Take It or Leave It. Time to sharpen your wits with Eversharp. Yes, it’s Take It or Leave It, presented by Eversharp, manufacturers of Eversharp precision writing instruments and Eversharp Schick injector razor blades.

I have found an early figurative use of the phrase in The Lincoln Star (Lincoln, Nebraska) of 31^st January 1941; in his column It seems to me…, Don Kellogg wrote:

Take it or leave it—the $64 question: Will W. H. Browne, Nebraska coach, return to the Husker institution to resume his duties after he has completed a year with the National Guard at Fort Robinson, Ark.?… We venture a “no.”

This advertisement for Potosi beer was published in The Democrat and Leader (Davenport, Iowa) on 25^th July 1941:

What’s the beer with old-time body and flavor?
Why Potosi pure malt beer

There is the sixty-four dollar question on any Quiz Show. Most everyone up and down the Mississippi knows by taste the fine flavor and full-bodied goodness of Potosi, the 100% pure barley malt beer.
For over 91 years, the master brewers of Potosi have worked their trade in the quiet hills of Wisconsin . . . turning out a better beer . . . a beer aged to delicious maturity.
Try a bottle of Potosi today . . . the beer that made the “Nineties” gay!

The phrase was soon developed to sixty-four thousand dollar question—more than a decade before The $64,000 Question, inspired by Take It or Leave It, was first broadcast on CBS television on 7^th June 1955; the following is from The Pittsburgh Press (Pittsburgh, Pennsylvania) of 15^th June 1943:

Sixty-four thousand dollar question: What do you think Jake LaMotta was doing in his dressing room immediately after his skirmish with Fritzie Zivic? . . . So help us he was shadow boxing, of all things! . . . We have this on the word of Zivic who dropped into LaMotta’s dressing room to congratulate him . . . Clad only in shorts and with both eyes practically closed from the pounding he had taken from Fritzie, Jake is reported to have been shadow boxing for all he was worth . . . “In all my life, I never saw a guy doing that after a fight,” the perplexed Mister Zivic commented.