I disagree with your premise about illegals taking the jobs nobody wants.
We have too many citizen freeloaders on our tax doles getting welfare checks for doing nothing. Take those welfare checks away from the able bodied freeloaders who are pseudo-disabled, and suddenly those unwanted jobs will be in demand again. Most of those so called unwanted jobs are unwanted because too many people just don't want to work. Why work when our government sends a check and food stamps out every month?
Since when did certain jobs become too menial for Americans to perform?
"I disagree with your premise about illegals taking the jobs nobody wants."
Illegals take all types of jobs whether it be in agriculture, domestic, or carpentry. I'll agee that there are far too many folks out there that simply don't want to work. Many however find it more cost rewarding by not working. Eliminate the freebies, increase wages to something livable (market wages among legal residents) and the illegal problem should go away for the most part.