We have enough space, but refuse to build affordable housing, for our citizens or for immigrants/asylum seekers. It's a fake problem conjured entirely from broken incentives and an utter lack of political will to fix them.
Many cities have overly-restrictive building codes that prevent adequate housing from being built, which raises housing costs.
Our immigration rate is too high for the amount of new housing units we build, which raises housing costs.
Many businesses have taken a hardline stance against remote work, even for jobs where it would make sense. That forces people to live in areas with inadequate housing, which raises housing costs.
Existing housing is being increasingly purchased by multibillion dollar companies for rent-seeking purposes, which raises housing costs.
There's really no one-size-fits-all solution to the problem, but slightly reducing the immigration rate, limiting corporate ownership of detached single family homes, incentivizing remote positions, and forcing cities to approve more new units would almost certainly improve the situation.
Before you go posting links about Social Security and Federal Taxes, it doesn't matter to local governments, they don't see that money. Also worth noting, Local Governments don't work like Federal Government, any debt they take on must be repaid on time or go bankrupt which is not good.
I understand that people are worried about this – and it's certainly an intuitive idea –, but is it true? I would count taxes on the total economic output / labour, not just the taxes from what is captured as salary (after all, underpaid workers make the world go 'round), but any analysis would do.
So sure, the entire US GDP and thus taxes is extremely reliant on these workers but who sees the benefits is not uniform throughout the country and thus the friction around immigration.
I don't know the solutions, I'm just aware of the problem.