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?
That doesn’t matter if minimum wage goes up. Like you said, a person can only eat so much. Rising prices are not a problem if wages (especially minimum wage) increase faster than inflation.