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People have all along presumed that the limit on population growth would be food or energy or space. Nobody realized that the limit would be usefulness.
Even in the US we have far more people than we can employ. There just aren't that many things that need to be done.
Neither the rich nor the poor will disappear, but the middle class will be increasingly unnecessary. The US will be nothing but businessmen, programmers, and government workers on top, and immigrant turnip pickers on the bottom. And of course the people below the bottom, those who have given up completely on the idea of being productive.
It doesn't help that gifted middle-class families have both mommy and daddy working, to gild the lily of American life and leave the children mommyless. There would be jobs for all the families if the daddies worked and the mommies took care of their families, or vice versa if you like. But they don't want to.