you want to say they won't work as productively/hard, or as cheaply as they would have to when you add millions to the labor supply, I wouldn't argue.

When you create a safety net that will pay you as much, if not more, to stay home than work (even more so when you factor in childcare and other expenses), common sense will tell you why "Americans won't take" those jobs. Furthermore, when you create a system that penalizes you for going out and doing whatever you can to better your situation via an at or just above min wage job, of course "Americans won't take" those jobs. Why go work for $1 if they will simply take $1 in "free" money from you? It's supposed to be a hand up, not a hand out.

Secondly when you import, or allow millions of low skilled workers into the country, simple supply and demand of labor laws will tell you those wages will be pressured to stay low or go down. Without them, and using less productive/hard working labor, yes, the cost of our apples, restaurant meals, and roofing jobs will go up. Or no longer kept artificially low as the case may be.

I do find it a bit ironic that the same folks that argue for keeping/allowing all these illegals which artificially keep low skilled labor wages down, then turn around and argue for a $15 Min Wage. Maybe, just maybe, if you didn't have these millions of laborers, wages would already be well on their way to $15, because that's what it would cost to get someone from the smaller labor pool to take that job. That's how the free market works.

Finally, if we truly have jobs "Americans won't do" after removing all the disincentives, an intelligently designed immigration system can address that. A merit based immigration system can just as easily give a preference for Apple pickers as it can someone that already speaks English.