TL;DR:
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The "myth of the 'temporarily embarrassed millionaire'" is not "a class-blind public". When Steinbeck said
"I guess the trouble was that we didn't have any self-admitted proletarians. Everyone was a temporarily embarrassed capitalist. Maybe the Communists so closely questioned by the investigation committees were a danger to America, but the ones I knew—at least they claimed to be Communists—couldn't have disrupted a Sunday-school picnic. Besides they were too busy fighting among themselves."
He was pointing out that nobody in America sees themselves as poor. My understanding is that this is common in former English colonies: while England is class-conscious, English colonies were established as places where scrappy young adventurers could rise above class to get them to come toil under horrific conditions. "Land of opportunity" means, effectively, you can rise above your station which sets the country up in an aspirational frame of mind.
Not that the British are immune.
What Piketty and Nancy Isenberg and many other academics have pointed out is that the American poor doesn't fully recognize themselves as poor so long as there's someone worse off than them. The Democratic project of the 20th century - equality and social projects - drove many poor whites to the Republicans because while white folk might have been a little better off, colored folk were a lot better off which ended up as a net loss of socioeconomic status.