Ok, well, anecdotally I'm hearing the opposite. :) Everyone I talk to recognizes the value of immigration generally and is focused entirely on illegal immigration.

I'm not just sharing anecdotes. Trump cut the number of refugees admitted to 18k in 2016, from 110k the year before. The focus is absolutely not just on curbing illegal immigrants, but also on limiting viable legal options.

So if the US immigration policy became "everyone seeking to immigrate gets a visa, pending a quick background check", they would be OK with such a policy? If the argument is just to end illegal immigration, then make all immigration legal. Otherwise, the problem is not just they're coming across the border without dotting i's and crossing t's. It's something else about immigration.

Most of the people in camps on the southern border are seeking asylum. That is an established legal process.

Nonetheless these people were demonized and subject to family separations and lesser cruelties.

Not everyone thinks that!