You said you're opposed to it, but that didn't jibe with your first sentence, which stated that demand for labor was their (presumably only) reason for coming here. And there's more than welfare on the other side of the equation; there's services - including health services that hospitals pay a huge price for - and crime. Not to mention the rapid growth of government that inevitably goes along with it all, and the balkanization of our society at a time when more than ever we need unity.
ALl expenses that they cant pay for that we the tax-payers have to pay for like health care and education should be denied to illegal immigrants. But, as long as they want to work they should be allowed to. There is not much you can do for crime other than prosecuting them. Even if you seal the borders, criminals would find a way to come where there is a bigher return for committing crime.