Some industries, like agriculture or restaurants, rely so heavily on cheap immigrant labor that enforcing this would cause an economic crash and food prices would soar. Other industries will ask prospective employees their SSN, which illegal immigrants don't have. So, which part do you wish to change?
You're saying the only way for America, basically the richest nation in the history of the world, to produce food is to rely on illegally paying and exploiting foreigners? How do all the other less rich countries make food then?
Illegal immigrants have many methods of getting SSNs. Like, it's not even difficult.
I'm saying that it's force massive changes, and, really, increase prices significantly (food is more expensive in Europe for example). Same in restaurants, you'd have far less staff.
It's not impossible but it'd have to go with cultural changes, and have a dire impact on poor people. Just because the US is rich doesn't mean it's working well, just look at healthcare and how costly and unfair it is.