Uh, in the housing that they build? The amount of housing we can build with cheap immigrant labor is so much more than what we can do without them. Housing gets more expensive when immigrants are pushed out, because the cost to build rises more than the reduced demand reduces prices.

Partly true, though to a first approximation, the reason we don't build more houses isn't an issue of construction labor costs. Many places with jobs don't allow building homes.

(That's not inherently a universal problem, especially if you're talking about the entire labor market. But it's a problem in many places.)