You want evidence of what? Of human nature? Do you sincerely believe that few illegal aliens are coming in for the generosity of the welfare state? Or that few are coming in for the great financial incentives involved in the drug trade? Or that terrorists haven't figured out that our porous borders are ripe for exploitation?
You're asking for evidence for these things, when you don't seem to require evidence to believe that such large numbers would cross the border if the U. S. economy doesn't grow at some particular percentage. And you want to believe that, regardless of any consideration of the relative health of the U. S. economy versus the Mexican economy.
They will come as long as they can displace American workers from their jobs, until the economy collapses.
But you demand more evidence than you're prepared to provide for your own claims. So, no soup for you.
Why is the unemployment rate under 5%? As I noted above, this is not a zero sum game. There are arguments to be made against such a large influx so fast, and about who makes up that influx (should it be titled a bit to more upscale immigrants?), but a collapsing economy is not one of them. It just isn't. To suggest otherwise, strikes me as more of a symptom of hysteria, than a serious attempt to wrestle with issues that have a real nexus to remotely reasonable assumptions
IOW, you pulled your former scenario out of your own head, and there is no evidence for it. That's what I thought.