Yeah, having lived in a low-20k-with-child household growing up, it's certainly doable, if not exactly ideal. You pretty much have to cut out car payments (a new car is not essential) and emergency money(it's a good idea, but also not essential), and your grocery trips are planned. The food isn't quite as good, either.
I don't think the issue here is the impossibility of doing this - a single resident can and could live just fine on, say 25k...it's that generally, no matter how much you make, your lifestyle expands to fit your paycheck. Partly that's because living on a budget is hard work, and the other part seems to be some sort of voodoo magic like the fact that living in an apartment with lots of storage space will magically increase your belongings to fill all the possible space.