This is another one of those asinine phrases that no one seems to ever want to back up.  They say that illegal aliens do jobs that Americans just won't do.  Which jobs, exactly, are they talking about?  The auto parts factory jobs they just arrested a bunch of illegals at a few months back?  The cook at the local Denny's?  The guys who do the landscaping in my neighborhood? All of this is a bunch of crazy BS.  Plenty of American citizens do those jobs every single day.  Thomas Sowell is right:

How many times have we heard that illegal aliens are taking "jobs that Americans won't do"? Just what specifically are those jobs? Even in occupations where illegals are concentrated, such as agriculture, cleaning, construction, and food preparation, the great majority of the work is still being done by people who are not illegal aliens. The highest concentration of illegals is in agriculture, where they are 24 percent of the people employed. That means three-quarters of the people are not illegal aliens. But when will the glib phrase-mongers stop telling us that the illegals are simply taking "jobs that Americans won't do"?

If you want to talk about people who will do jobs for less that the prevailing wage for which Americans will do that job, then fine.  Even my job can be done more cheaply in India.  But to say that illegals do jobs that just plain would not get done is both insulting to us and them.