There are only 2 million unemployed Americans right now. Most of the illegal immigrants have jobs and fill in the gaps, such as working on farms and factories. If the 20 million illegal immigrants are deported, want that create a massive laborer shortage? Won’t the work follow the workers to Mexico?
If the USA can get foreign workers willing to do those jobs for very low wages, paying Americans a lot more money to do them seems like a waste. I think the situation is similar to the outsourcing of American manufacturing to other countries. The main difference (other than the fact that one involves sending jobs elsewhere and the other one involves bringing workers here) is that the move to a post-industrial economy hurt those Americans who worked in industry even as it made the average American better off, whereas Americans already don’t work in agriculture so a guest-worker program would maintain the status quo there while restoring the rule of law.