I think that's why framing the debate is so important.

1. This isn't magically closing the border, this is just adding a new punishment for a small subset of people who cross illegally. Whether or not it will be effective is very debatable (if barbed wire doesn't...)
2. We should be talking more about the backlog in asylum cases, why aren't we providing adequate funding for the courts to do their job.
3. Why do we make asylum seekers wait so long to seek asylum and get authorization to work, how does this do anything but place a burden on support systems?

And so on. This isn't about stopping immigration, it's about punishing those who do. [Too] Many will still support that, but it's a harder stance to take.

Since many migrants often work construction etc. Perhaps they could be employed to build it. Just a rational stab in the dark here.

And yes we bitch about rent etc. The key thing to understand, is that rent doesn't really have a reason to cost as much as it does. The actual cost of upkeep etc for the buildings and property etc is a fraction of the rent. We've as a society demonized public housing, and largely refused to let any new be built. Or take care of the few that have properly. Because "reasons".

Democrats moving to the right to try and get republican votes isn't a great strategy. But they'll get to blame the left if they lose, and keep moving to the right if they win. Billionaire donors stay winning.