I've always wondered what the net impact is of illegal immigration from a pure economic standpoint. And while I have read a lot on the issue, I don't have a conclusive opinion. I will point out a few things though. These are all from memory, so I could be wrong on these facts:
1. There are different types of illegals. Many of us are envisioning border jumpers from Mexico who don't speak English, and there is certainly an epidemic of this happening due to the insanity of drug-cartel run Mexico, but more common than that are visa overstays. These are folks from all over the world who arrive by plane, with permission work in our country for a certain amount of time, but just don't leave when they are supposed to. They pay taxes into our system.
2. The biggest drain of illegals is emergency healthcare, education system, prison system - way more than individual programs like welfare, food stamps, etc.
It's a very intricate, detailed issue. Here is an interesting case study on Arizona which got rid of a lot of illegals (by requiring verification to employ them) and lots of them left/were deported, and many different aspects of the economy suffered as a result.
TLDR: First, there are the businesses like landscaping that run on these guys. Second, these guys consume - food, clothing, shelter etc. And removing them impacts those industries. There are public savings costs that are harder to quantify by removing them from ER's, the kids from schools and prisons.
ETA i removed the arizona link, was the wrong article.