Consider:
What Ms. Cash is saying is that she thinks that the amount of work she does must determine the wage she is paid. But not even Karl Marx thought that! In Capital: A Critique of Political Economy - The Process of Capitalist Production, Marx gave this explanation:
Karl Marx Some people might think that if the value of a commodity is determined by the quantity of labour spent on it, the more idle and unskilful the labourer, the more valuable would his commodity be, because more time would be required in its production. The labour, however, that forms the substance of value, is homogeneous human labour, expenditure of one uniform labour power. The total labour power of society, which is embodied in the sum total of the values of all commodities produced by that society, counts here as one homogeneous mass of human labour power, composed though it be of innumerable individual units. ...
... The labour time socially necessary is that required to produce an article under the normal conditions of production, and with the average degree of skill and intensity prevalent at the time.
[Following is the key point:]
The introduction of power-looms into England probably reduced by one-half the labour required to weave a given quantity of yarn into cloth. The hand-loom weavers, as a matter of fact, continued to require the same time as before; but for all that, the product of one hour of their labour represented after the change only half an hour's social labour, and consequently fell to one-half its former value.
What Marx was saying is that as efficiencies of production increase per unit of time, the value of the labor of the "old" production correspondingly decreases. When powered looms in England doubled the rate of production, the labor value of the prior manual production decreased by half.
What Ms. Cash and her allies need to understand is what needs to be be said over and over: the actual, real-world minimum wage is $0.00.
When she gets a raise to $15 per hour she will not increase her production of product. When McDonalds figures out that her work can be automated - as has already happened with electronic ordering kiosks replacing human order takers - the wage value of her work will go down, not up. And she should not be surprised when her wage then drops to zero because her old job is being done by a smart machine for an amortized "wage" of less than $15 per hour.
