I went through the entire comment thread and feel like you guys are missing a lot of the H1B benefits by focusing just on tech and the effect of the Indian consultancies. Most PhDs, specially in STEM, math, stats, econ, etc. are not American. And almost all of them end up with a H1B visa at some point if they remain in the US. It might be lottery based if you go to work at any firm, or quota-free if it is in academia…
I don't know of any serious active effort to kill the H1B. I think that would be a disaster for the tech industry as large companies like the ones you mentioned rely on foreign talent.
The only effort I'm aware of is to raise the minimum salary to qualify for an H1B. Right now, the minimum is $60k, which, in the US, is very low for a legitimate programming job. I'm certain that H1B workers at Boeing or Amazon are getting paid more than the minimum right now. However, there do exist shops out there who exploit H1B visas for cheap labor; I've experienced them firsthand. They aren't as uncommon as you might think.
There is talk of raising the minimum to something like $120k. Surely, a PhD trained researcher at Boeing or Amazon is worth at least that. They are probably already getting paid the prevailing wage for their labor, which is a legal requirement of an H1B. In these cases, raising the minimum will not affect them at all.
Recall that the original purpose of the H1B was to fill a demand for high tech, specialist roles. Is there any high tech, specialist role that is only worth $60k these days? I don't think so.