The Mexicans accept this lower wage because they can live on it - at 15 to an apartment or something like that. Americans won't work for a salary that forces them to live in such dismal conditions.
If the employers who hire these muchachos are paying them at least minimum wage, then the problem is, indeed, a labor shortage. If they are paying them less, then it isn't a labor shortage, but a desire for cheap labor. In that case there will always be a market for illegals.
In my line of work, there really is a shortage of good people. If I'm on a deadline to have a project complete by a certain date, or face penalty pay....I'll hire whoever I can get. The problem is that many of the American workers in this line of work (not all mind you) are not that dependable. Most want excessive money, rarely do they stay throughout the length of the project, and most are either drunks or dopeheads.