During my career I have worked for less than "minimum wage" at times in the past but I was accumulating skills that I believe benefited myself and my future employers. I now earn considerably more than minimum wage but I "earned" it, it was not given to me. 
Now, every time the "minimum wage" is artificially increased, it is a direct dilution of the wage that I have earned. This country cannot afford more people with no jobs because their skills do not equal the cost to hire them. They do not have the opportunity to learn the job skills needed to be productive workers. 
Minimum wage laws just compound and increase the cost of living problem for every one, but especially those people who do have the lower paying jobs. It is just a vicious cycle that hurts the people the most that it is supposed to be helping.