Your premise is wrong. There are not 20 million Americans "Waiting for jobs." That's the whole issue. See the video about "Julia." That is the mindset. Let the government take care of it. The problem with illegal immigration is that too many Americans are not waiting for jobs, they are waiting for checks.
Seriously, how many folks do you know who are waiting for jobs picking veggies, mowing grass cleaning up buildings? Huh? How many? Zero.
There is no "mindset" when you have 53% of all recent (last 5 years) college graduates unemployed.
Working with big numbers is difficult for some people so they want to believe all these people are just ditzes, or greedballs ~ but I KNOW PLENTY OF THEM! And that's even in NOVA where we have 4% unemployed ~ which is about triple the numbers normally unemployed in this area ~ and they're not waiting on handouts ~ they're living in basements and find themselves competing against every unemployed person in America for whatever jobs are available around here.