It's a very complicated issue. While the process of becoming a citizen is extremely complicated and in some cases almost impossible I think that it's almost more of a pragmatic decision on the part of the U.S. government than anything else. The developed world's wealth relies on the poverty of the developing world. I'm not a Marxist, but even I realize that my quality of life in the U.S. would be much lower were everyone in the world to have a fair shot. Also the limited amount of legal immigration and naturalization allows for only the best and the brightest of the developing world to immigrate. This further perpetuates the poverty of the poor by removing their fellow countrymen who could actually contribute to the growth of their own economy.
Illegal immigrants, specifically from south of the U.S. border, fill a very important role in the U.S. economy. Despite what many may think of them as just simply plundering the economy, and running home to Mexico. They often do the jobs that U.S. citizens see themselves as too good for such as construction, busing tables in restaurants and washing dishes, mass agriculture, and many other things. But I would also like to point out that while this system is corrupt in many ways it also has advantages for many illegal immigrants. In a restaurant a dishwasher could become a chef, or a construction worker could become a foreman. These realities exist, and I've seen them time and time again usually because the possible chef has proven to be a skilled and reliable worker that would work for less. However, as you can imagine this has a negative impact on many skilled workers in the U.S. chefs in chain restaurants like Chile's make nothing in the southwest, because an illegal immigrant who is maybe in the process of naturalizing or has just been around a while will work for less and communicate more efficiently with the kitchen staff who mostly speak only Spanish.
Although many point to smuggling and the drug cartels as a major part of illegal immigration from what I've seen I tend to disagree. I also believe that if legal immigration were expanded upon that the cartels would be easier to pick out. If someone noticed someone trying to smuggle across the border it would probably be more likely to be a smuggler rather than just another illegal immigrant. Also the extensive border is really almost impossible to completely wall off and restrict immigration. For those of you who are Canadians can you imagine the logistic that would be involved if nearly every American citizen who wasn't eligible for Canadian citizenship wanted to sneak across the border to Canada? There's not enough people in Canada to stop them! To be fair the border with Canada and the U.S. is a bit larger than the U.S. Mexico border, but not by too terribly much.
In other words, I believe that were the U.S. to make the correct moral choice they would expand legal immigration tenfold. However, if the U.S. were to make the pragmatic choice that would benefit its citzens the most, then I would do pretty much nothing and just pretend to do stuff when the public was riled up about it. As far as those American born chefs and construction foremen who have lost their jobs to cheaper labor? Well, I suppose they can always join the army. *wink, wink, nudge, nudge*