The author of this Slate article makes a good point about the reason
you don’t see many Americans doing entry level construction, fruit
picking, or landscaping work:

“It’s not so much that Americans aren’t willing to pick fruit and
become computer programmers. Rather, they aren’t willing to do those
jobs for the prevailing wages and benefits.”

What the author fails to point out is that this unwillingness on the
part of Americans to do such jobs at the prevailing wages is not a
problem to be solved, but a result of the labor market.  When choosing
a career path, Americans choose what they believe to be the best option
among many alternatives. It seems many view unskilled labor as an
undesirable alternative.  

In turn, employers act in their own best interest by seeking out the
most cost efficient labor available among the alternatives.  It
seems the most cost efficient pool of workers they have found is
comprised in large part of illegal immigrants.

As long as the risks involved with hiring illegal immigrants are low,
employers will continue to hire them.  Illegal immigrants will continue to work in unskilled jobs–yes, at
lower wages than most Americans would be willing to accept–because the
wages they receive at those jobs, though low relative to, say, a computer
programmer’s, are the best among their alternatives.