...the "solution" proposed is some kind of amnesty. That's what Miller and others object to.

I think you're wrong.

Not that they don't object to amnesty - they certainly hate amnesty with the fire of thousand suns.

But there's no indication that they're any less hostile to a guest worker program. Recall the conflict over the H1-B visa program that happened early on in the administration. Musk was on the side supporting the program, and it was Miller (and Loomer and Krikorian and the other MAGA hardliners) pushing back hard against it. Musk prevailed in that conflict, but it certainly showed where the lines were drawn. Krikorian hates even the H2-A program. And you saw how they pushed Brooke Rollins from where she was advocating for farmers to be spared the whip on immigration raids earlier in the Administration to now claiming that those workers will be replaced by citizens that lose their Medicaid.

There's no way that this Administration "expands programs like this" as long as Miller's holding the policy reins on immigration matters.