In the CIS Policy Journal, former Chairman of the Australian Fair Pay Commission Ian Harper raises a second best argument in favour of his having raised minimum wages occasionally. Specifically, if welfare benefits are too high, then too low a minimum wage can encourage too many people to stay out of work.
I'm having a hard time making sense of the argument. It posits a situation where the minimum wage is below the worker's reservation price, because of the welfare system, but where the value of the worker to the firm is higher than the worker's reservation price. Otherwise, raising the minimum wage just means that the worker is involuntarily unemployed rather than voluntarily unemployed. But if the value of the worker to the firm is higher than the worker's reservation price, he'll be hired regardless of the minimum wage being lower than the worker's reservation price.
Maybe you could specify a continuum of reservation prices such that there are lots of folks willing to work at a low minimum wage, so the high reservation price guy isn't brought into the market because lower cost workers are available, but that would require a monopsony assumption (otherwise workers wages are bid up to marginal value and anybody whose marginal value to employers is higher than reservation price is employed).
Having a hard time seeing the second best case here.