Why is this true? It's not a natural condition. The natural condition of a free market is an equilibrium between supply and demand. If you have excess supply, it means the market is not at equilibrium, which means either (a) it's in transition because of some recent change (not likely since the oversupply of low-end labor has been around for quite a while), or (b) the market is not free--something is skewing the supply-demand balance. The obvious candidate for that is...existing minimum wage laws.
> The minimum wage is just a needed correction for this oversupply of labor
Raising the minimum wage will not "correct" the oversupply of labor; it will make it worse. There will be more people wanting jobs, and businesses will be able to afford fewer of them.
That's the natural condition of a theoretical free market, real markets are not theoretical. As Keynes said, the market can stay irrational longer than you can stay solvent.
Also, poor people have more children than rich people.
They very often aren't, that's true. And in many cases, that's because real markets are not free markets; they are skewed by government intervention. The market for labor in the US, and indeed in most countries, certainly fits that description.
> As Keynes said, the market can stay irrational longer than you can stay solvent.
Yes, and he did his level best to make that prophecy come true by getting governments to intervene to keep markets irrational.
> poor people have more children than rich people
How is this relevant?
A million things skew the labor market away from the theoretical: people are irrational, information is wildly asymmetric, wages are sticky, there aren't an "arbitrarily large number of firms", the factors of labor (people) aren't liquid or mobile, etc.
To pick 'price floor' from the long list of things that distort the labor market while ignoring the rest is strange enough that I chalk it up to politics any time I hear it.
The model I'm describing, while it is certainly an idealization, is not for that reason inapplicable to the real world. Idealized models are useful in understanding the underlying factors at work in a real situation, even if the real situation contains other factors that are not modeled. Often you can add those other factors in as constraints (for example, there's no reason why a microeconomic model has to assume "no minimal sustenance"; you just add the minimum requirement for sustenance as a constraint). Or you can expand the model to include interactions that were not previously captured (for example, if waste disposal is a significant factor, you can expand your model to include the economic transactions involved).
You misspelled "excessive constraint of demand caused by a debt crisis driven by a criminal financial sector".