Why? There's nothing preventing citizens from standing at Home Depot parking lots to do illegal cash jobs.
I'm willing to bet that the vast majority of the "under the table" work in this country is done by citizens looking for some extra work here and there or freelance.
The big advantage most illegals have are a community support system and family. Most poor citizens don't have that kind of support, poor black communities are a good example. Compare that with immigrant communities elsewhere. When my father came to this country, people from his village or nearby areas who were already settled had connections and even a place to stay while he got situated. Loans etc. Mexican and Chinese illegals have the same. Poor Americans do not because if they did they wouldn't be poor in the first place.
You can work off the books for a while and send a portion of a week's pay to poor countries where that money can feed an entire family for a month, or you can be a citizen that has to support his family stateside, without the other benefits of a large immigrant community.