One more point on all this. One response might be "well immigration reform is really hard so you should take what you can get". Maybe. We still seem more welcoming to immigrants than much of the world, and it seems to me we can prevent more hardship by focusing on what enforcement is doing to lower skill immigrants. But you might be convinced by this argument for focusing on high skill immigrants because that's what we can get done.
But glossing over the economics of the S&E labor market for policy reasons because "we can get something done for high skilled immigrants" is misleading, I think. It's about a lot more than immigration policy. When you validate this idea that we have a shortage of scientists and engineers, or that the labor market for these types of workers isn't up to the task of providing the country with what we need, you get domestic science and engineering labor policies too that try to tip the scales in favor of producing more and more of these types of workers.