Few? Really? Then...then...who's doing the work "Americans won't do?" If there are "few" Illegals working...then how are they "earning" a living?
Do you have any idea of what a large company is? Or if they have more than two people they are large in your world. Going beyond the companies, many of the people working in agriculture, or moving lawns, or working as nannys or cleaning ladys are working for individuals, not corporations. If these people want the work done they are going to continue paying them under the table.
OK...background...I'm a Pharm Chemist, and have worked for the largest Companies in the US and World.
1) There were Illegals on site. Note, we were a "secure" facility, I worked on Nuc Med....and there were ILLEGALS running around in the Labs and cyclotrons and Isotope Storage areas! When WE were not there! Does THAT scare you? Because it should! What about the Illegals being caught being employed by Contractors on US Military Bases? Is that cool? Are THOSE the jobs "Americans won't do"?
2) Maybe YOU need some "edjukashun"...if you work, you need to have a W-2 and a W-4...right? When you are hired, you have taxes withheld....THAT is how you cross-check. Oh, and if they are "under-the-table"....isn't THAT "Illegal"? Shouldn't the Illegal Infiltrators "doing the Jobs Americans Won't" have to pay TAXES on those jobs? Or are Illegal Infiltrators exempt from that too?
3)Any "Contractor" should have to report their "employees" status, and the Company contracting them should stipulate in the Contract "No ILLEGAL LABOR"! The Contractor that violates this should be fined/imprisoned/confiscated.
See, your way artificially deflates the wages...but you are OK with that as long as the lettuce is cheap, and the toilet scrubbed, and the lawn clipped!
What you fail to realize is "Illegal Labor=Slave Labor"!
Try and refute any of this....