Until you look a little deeper. High tech industries are an excellent example. The system already exists in that industry through the H1B visa game.
Employers have easily shown that Americans don't want the jobs. Americans don't want these high tech jobs because the wage has been artificially depressed by the employer below the level that the American worker can economically justify.
That same manipulation of an honestly constructed system will be applied to all other industries. If you want foreign workers, simply cut the wage in half and you can have all you want.
Who benefits? The foreign country. Who loses? The American worker who was forced to pay thousands for his technical education only to be denied employment because of an excess of cheap, equally well qualified, foreign labor.
That is not to suggest I am a big fan of H-1B visas. I think that if there is a 'shortage' of technically capable people, then wages should go up and more people will then train themselves and educate themselves to get those jobs which would expand the work pool and allow wages to come back down; I don't think the answer is to expand the work pool artificially by importing tons of foreigners. But it is a different issue.
So the question becomes, are wages be depressed in these jobs that illegals are currently working (which tend to be lower paying ones) by them being here by more than the amount of added cost there will be in ensuring that the p's and q's are taken care of in meeting the requirements of this law? I am skeptical.
Besides, I still think people are overstating how many current aliens would take 'advantage' of this system. Let's say I am an illegal immigrant. I took a job with some forged papers. I want to take advantage of this, so I don't have to worry about being caught. I go to my employer, and now my employer (who for me to become legal has to vouch for the fact that there was no American who wanted my job) has to decide if he is going to fire me for lying about things in the first place, and then may end up finding some American citizen to take my job, the very job I need to stay, in order to meet the criteria specified. I bet the percentage would be small.
But there is still my main concern, the concern I have which tells me this whole thing is a bad idea. The fact that judges could gut the good parts of any such plan, leaving only the garbage. It is too big of a risk.