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?
Rising food prices don’t just affect poor people, they affect poor people far more than they affect rich people. After all, a person can only eat so much no matter how rich he is.
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.