The biggest problem with illegal immigration stems from people who enter here with no intention of paying taxes, yet abuse all the systems paid for by the American taxpayer. If there was no monetary incentive to illegal immigration I don't think as many people would care about it.
However, when financial stresses are put on local governments dealing with large illegal immigrant populations, schools who are educating children without receiving the tax dollars from their parents, or hospitals throughout the country having their ED's busy with non-emergency care seeking illegals it stresses the American system in ways that many taxpaying citizens feel is unfair. If the United States were abusing other countries' systems in the same way, I would expect the other countries to take issue with our illegals. Yet, I cannot think of a country where American citizens are entering illegally and receiving benefits without paying for them, while at the same time expecting the citizens of that country to foot the bill.