You can't claim that only Americans are unwilling to work the jobs at the low wages that illegals will. Here's some (thousands) of Mexicans who won't either ---they're demanding more welfare instead of heading to the fields to pick chilis or bale hay.
http://www.tradeobservatory.org/News/index.cfm?ID=4476 They're actually suing the government for more handouts and they consider it discrimination to offer English as part of job-retraining. You certainly won't see them competing with illegals ----and yet they have the exact same language and job skills and came from the same place.
You can't claim that only Americans are unwilling to work the jobs at the low wages that illegals will. Oh I don't. Lots of people of all nationalities seem to believe that they should have protection from free competition and protection from what happens when you don't work. I am for ending federal government welfare as well as for ending federal government protection of jobs. I waste tons of money on both, and so does every American.