I came here with my parents, who emigrated from the former USSR via the student visa route in 1992. This is one of the hardest paths to permanent residency in the US because a great deal of student visas either explicitly foresee a return of the student to their native country for some period of time (owing to various reciprocal treaties to that effect), or are implicitly structured to discourage permanent immigration per se.
Somehow, my parents defied the odds, frequently hopping between various F, J and H-class visas, begging for employer sponsorship through these processes in an already grossly unfavourable job market (humanities academia). In at least one case, I remember that making changes to visa status before the existing visa expired required short-circuiting the INS bureaucracy and going to the US consulate in a Mexican border town to get the job done--ironically, much faster.
It wasn't even until 2002--a decade later--that we had a greencard. Up until that point, if my dad had been dismissed by any of his employers or lost his student for any reason, we would have had to return to our country immediately, from where trying to seek new opportunities along these lines--especially in the 1990s--would have been impractically difficult. Worse yet, a petition for a greencard from many classes of visa means that if for some reason the petition is denied, you forfeit your existing visa and also must leave. And of course, employer sponsorship was required.
We finally became naturalised US citizens in 2008, 16 years later, well after I had spent close to 3/4ths of my life here. And many commentators who work with people in our situation have remarked that this was brisk and efficient.
While I am definitely speaking from the vantage point of a particular visa classification and method of entry, I don't gather that our situation is that uncommon. The number one problem that I see with American immigration from an economic perspective is that it's simply too hard to immigrate here (legally)[1], and most especially as a highly educated or highly skilled person. Marrying an American or obtaining a refugee status of some description is a much more efficient path to permanent residency, for example. Meanwhile, a person with an existing PhD like my dad had to essentially get another PhD to become employable here[2], while persuading employers all throughout to argue that there no equally suitable American candidate was found for his job, etc, etc. I have not seen janitors face such hurdles.
I will freely grant that it's not nearly as hard to immigrate to the US legally as it is to say, Western Europe, but it's also not as easy as Canada or some other Western countries whose immigration systems admit an explicit preference for high qualifications. And as the author points out, with domestic economies becoming more and more attractive, it just isn't worth the effort to fight with this immigration system like it used to be.
EDIT: To relate this back to Vivek Wadhwa's article: We come from Moscow. In the early 1990s, following the dissolution of the USSR, Moscow was a pretty miserable place to live. Coupled with the enthusiasm to leave the Soviet context in general, the appeal of America was pretty clear. Nowadays, Moscow is not a particularly miserable place (although the reasons for that, and the question of whether they are good, sustainable reasons, are a separate discussion entirely), and few people in Moscow, whether part of the noveau elite or otherwise, are deluded with the idea that they can find a better life in America--they already live in a gold-plated bubble rapidly coming to rival Manhattan sensibilities. So for whom does the US remain an attractive destination in Russia? Mostly provincial, less-educated people from poorer, simpler places. I read Wadhwa's article to be saying that--extrapolating from this more generally--this does not set up the incentives we really want.
[1] I found this chart from Reason Magazine to be a pretty accurate illustration of the problem: http://reason.org/files/a87d1550853898a9b306ef458f116079.pdf
[2] Yes, that's technically a separate issue from immigration policy and is rather tied up in the specificity of his profession, but if you want to talk about the amount of mountain-moving required to move to the US permanently, as a whole, it deserves consideration.