The way to sell Housing First is to show how it can be cheaper than what we are now doing.
When you add up the cost to city police, the courts, and the local hospitals it could be less than building housing.
Appeal to their fiscal concerns.
Kinda the way cannabis laws were sold to conservatives, you can tax it.
The problem here is the "siren maintenance problem" or "The IT Issue"
Once you actually start doing it, people start to look at how much of their own budget they spend on the housing (the vast majority of it, for the most financially insecure, and a HUGE chunk of not a majority even for the financially secure), and they see the price tag for that.
The issue here is that because they see a price tag, and there is no line item to offset that cost in their math (because by now they have forgotten all those unrealized costs in terms of homeless people healthcare and police action and so on), they say "how can we afford this", conveniently having forgotten how much it cost before, as the police and healthcare consequences leave from our awareness and only the line item for the housing remains.
A similar problem happens with siren maintenance: you maintain and install a siren in a community, test it once a month, and people start to question why the only time they ever hear it is in a test, and why we are making everyone annoyed and paying someone to turn a crank to do it. They say "there hasn't been a major emergency here for a decade, why do we need the siren and all that noise?!?"
The problem even pops up in IT and technology roles in a company: no downtime means IT is at risk of being let go. If IT is let go, there will be huge amounts of downtime. Therefore IT needs to strategically allow brief periods of downtime to prevent long periods of downtime.