I read this in The New Yorker. It's well written and, as the headline suggested, it does provide "the real numbers on illegal immigration."
But I dislike this kind of writing. The author takes a very serious tone and, early on, demonstrates command of the facts. You start to trust him. If you don't know any better, you continue to.
Then he claims that deporting illegal aliens would be "economic suicide . . . since they are, for a start, essential to large sectors of the economy, beginning with the food supply." But that is nonsense. If illegal aliens didn't pick fruit then farmers would have to pay for citizens to do it, or buy machines. Someone would have to produce the machines. Suggest that cheap labor is irreplaceable is irresponsible.
He also writes that "the Fourteenth amendment . . . guarantees citizenship to any child born on these shores." That is one standard interpretation of the Fourteenth amendment, similar to the interpretation that the 2nd amendment allows for possession of any type of firearm without restriction. Both of those are questionable, certainly not the intent of the authors, and probably not the interpretation you'd get from some random person in Wal-Mart.
The article ends with a series of attacks against "demagogues" after briefly dealing with one of the three hard questions in immigration reform, "don't illegal immigrants drive down wages for Americans?" That is what supply and demand predict, but (1) that doesn't tell you the magnitude of the effect and (2) things are more complicated. There is a large and growing literature of good research on the topic (see here). It would have been nice if he cut the attack on the nebulous "right wingers" and dedicated a few paragraphs to this issue. He could have also addressed these hard questions:
1. what penalty should they pay to gain citizenship? what is fair?
2. why should Mexicans get preferential treatment in immigration?
That said the first few paragraphs are worth reading.