But right now there are also shortages of available housing and sky high rent price levels. Adding more people is not going to help that issue.
Does the country really need more immigration at a time like now?
Remember, a lot of these immigrants are poor and can't afford to pay for new housing. So they will be instead taking up the already existing housing, especially at the lower end, and that's going to exacerbate the shortage of affordable housing that already exists.
The housing shortages affects the poor and the young adult generation the most. This population is also the least likely to buy a newly constructed house.
Land costs also make up a significant percentage of the cost of a house in some areas. In San Francisco, for example, the land underneath the house costs several times more than it would cost to construct a new house. That means that even if immigration might decrease construction costs a little bit, it would be unlikely to have much effect on lowering new home prices, when the main issue is availability of space to build on, not the cost of building.