I'd like to add some benefits not yet mentioned in previous posts.
1) Immigrants do actually pay taxes - those with functional Social Security numbers file income tax returns like everyone else. It's true that some do not pay income taxes and work under the table, but all of them pay sales taxes, gas taxes, property taxes through rent, and Social Security and Medicare taxes that are taken out of their checks. Keep in mind that for Social Security and Medicare, they will never see those benefits, but they pay into them every month. So they are actually helping us to keep those programs solvent, as without their tax contributions, they would be farther in the hole in the next 20 years
2) Much of the food you buy in the stores is cheaper because of immigrant labor. They work the difficult and sometimes dangerous work in fields and factories for less money and no benefits, while American workers turn those jobs down. Because production and harvest costs are lower, the savings are passed along to us at the supermarket and store, where we essentially get a tax break of savings every time we make a purchase.
3) There is an increased load put on social service agencies, schools, and the health care system, but as stated earlier, they already pay taxes for some of these services.
4) Some of the best minds in history have come to us through immigration. Albert Einstein, for one. They bring their intelligence, and art and culture and talent to us and we see the benefits, though they might be under the surface of what we would notice.