Just watching Advise and Consent (1962) and at one point Walter Pidgeon’s character says to Peter Lawford, “How about your friend Brig Anderson? Think he’ll jump the whale?” Pidgeon means will Anderson support the President’s unpopular choice for Secretary of State, Robert Leffingwell (Henry Fonda). The meaning of the phrase seems to be something like take the giant leap, make the big decision.
The only relevant reference I can find by googling the phrase is an identical question by someone else who saw the movie (although they get the speaker wrong). They don’t appear to have been answered. Anyone else come across this?