a “put your money where your mouth is” fallacy
Is this a “fallacy” or is it an “angle”? Probably it is little more than straw-man attack, because you know even homeless people need actual homes not just places to crash, and it is also a form of ad hominem attack that typically targets progressive/social change demands (do you really hear that often the opposite, like “if you hate homeless people that much, why don’t you support gassing them?”). I don’t know if people call those fallacies these days, I tend to see them as tactical conversational attacks. A fallacy is sth you can easily fool yourself with.
Fallacy means sth in the effect of “cognitive illusion” as in “logical fallacy”, not a rhetorical strategy. The difference is the intent of the speaker. A rhetorical strategy can be deceptive, or tactically motivated, a logical fallacy is more like a form of apparent naivete and common paradoxes. When there is intent to deceive and/or win at all costs, there is “prevarication” or “sophistry” instead of “fallacy”.