Let me re-phrase that for you:
You need to become competitive with people who are breaking the law or find something else to do.
I was the only white guy, save the boss, on a crew of landscapers for 3 years, in my twenties. Illegal immigrants aren't really the problem, the problem is a desperately inefficient and unrealistic immigration or temporary worker program to process all these folks gaming the border. Again, in my early thirties, I found myself the only white guy among day laborers on the street corner (or temporary agency).
No, I wouldn't take that $7.00/hr work now, I don't have to. However, if I needed it...I'd stand my lonely white @ss out there again in a heartbeat, $$ under the table, to feed my family. Wouldn't be the first humble pie I've eaten.
The solution ain't enforcement, its common sense to deal with the labor demand. Illegal workers wouldn't be here in the first place if the work wasn't available. They're meeting needs, and as long as the need is present, they'll be there to meet it.