There is no hypothetical sector just waiting for workers to move to. Manufacturing had always existed and grown steadily so long as the food needs of the population were being met by fewer and fewer agricultural workers. The shift didn't sneak up on anyone.
Those "historic low" jobless rates are much lower pay and skill on average than 10 years ago. Over the last 50 years people in those low-skill jobs have (when adjusting for inflation) been steadily making less money. We've reached market saturation on workers needed to meet the demands of the population.
I'm one of those people automating things. The really scary part is how much more quickly those of my ilk can automate processes now than even a few years ago. Expect the drop in demand for human effort to get worse exponentially.