That's not middle class in traditional class terms (petit bourgeois) based on the manner of interaction with the capitalist economy, but it's pretty much requires being “middle class” by the modern American broad income categories standards, where middle class is the middle income category.
That seems extreme.
No, I'm saying that people who are below the middle income category (as that adjusts locally) often cannot reliably, securely "afford someplace relatively clean to live, feed themselves, afford heat in winter, etc.". I'm not saying that they should accept that, just that if you are advocating for a living wage, you are, in fact, advocating to move the floor up to something that fits what is commonly styled "middle class" income currently.
I guess one factor here is "middle income range", if well defined, will move if the floor is moved. In things like this, distribution is also very important.