I'm not sure I buy this argument. From the point of view of an American, doesn't that mean that there are 1000000 fewer "unemployment openings" available? It would be like making a million jobs, except most of the jobs vacated probably suck. But I don't actually know that.
Let's say you hire a Contractor to repair roof damage after a storm. The Crew is Hispanic, most having their Greencards. They've been doing this kind of work for a decade. They get paid by the job, so it is in their interest to work faster, to get more jobs done. It is also in their interest to work well, so the Contractor doesn't start calling other crews instead of them.
Suddenly the Crew has half their members detained for minor criminal matters. Drunk in Public. Disorderly Conduct. The Rest of the Crew is now nervous and under strength. Hire Americans the morons shout.
Well Americans don't want to show up at six in the morning and work until six at night. They want an eight hour day. They object to the hard hours of lugging lumber up a ladder and don't work as fast as the Hispanic they replaced.
The Contractor has to pay more for this American. Because the American doesn't understand if he can get the job done in two days that is better than a week. Crews start to dry up, and the Contractor can't take new jobs because he can't get the old jobs done.
The same is true for Farmers. You have a field full of Watermelons. You want them harvested so you can ship them to market. Only the seasonal labor you would hire is gone. The Market will pay only a set amount, and you can't afford to bring the crop in at that price with local temp workers who are inexperienced and unmotivated.
I'm not saying it's good or bad. I'm saying this is the real world. Contractors will be changing their rates, because they are not going to lose money on a job. The people they hire will be desperate for jobs, and that means that it will mostly be made up of Ex-Con's who don't have a choice but to work in menial labor jobs. Of course when they get paid they'll spend most of their money on drugs and liquor which means the next day's labor will be sporadic and of uneven quality. This was a problem in Russian Factories during the Soviet Era and even today.
The Lada factory would start the assembly line slow, because the workers were either still drunk or hung over. As they sobered up and started feeling better the speed would increase through the day. Until the next day when it was again slowed down because the workers were drinking heavily at night.
American factories had similar problems. You didn't want to have your car built on a Monday. The Workers were usually hung over, and more defects were found in the vehicles being made. You could argue that the people should be fired. But eventually you run out of people to fire as you have to hire and train people how to work on the Line and it takes time to build experience and speed.
The so called simple answer of pay more and so forth is sort of like a story that begins. "Once upon a time" and ends with "happily ever after".