The most effective way to limit immigration is to assure the immigrants the rights Americans have. If their labor weren't quite so cheap, there wonuldn't be quite so much incentive to hire them, and fewer would come. As to those who pretend to be morally indignant about the "illegality" of it all, I would be more impressed if I were persuaded they themselves would never break any law--even say, if it restricted broperty rights or gun ownership.
Illegal border crossing should be discouraged, but it isn't particularly immoral. It shows initiative. Don't Americans, especially conservative Americans, admire initiative? Aren't Americans supposed to believe in democracy--meaning equality? What I find morally reprehensible is the idea of creating a brown-skinned lower caste with no rights. So if the question is, should immigrants be given citizenship--even without going home and paying five thouwand bucks that they don't have, then sure! They should have citizenship, if they want it and will do what it requires.