I think minimum wage is supposed to enable you to move up and not a wage where you can lead a comfortable life. It's expected that a single person on minimum wage can't get a two bedroom house.
> no business which depends for existence on paying less than living wages to its workers has any right to continue in this country.
> By ‘business’ I mean the whole of commerce as well as the whole of industry; by workers I mean all workers, the white collar class as well as the men in overalls; and by living wages I mean more than a bare subsistence level — I mean the wages of decent living
So no, the minimum wage is supposed to be a living wage, but has fallen far from its inception.
You can argue whether it's necessary that we have a minimum wage, but not what it was conceived for.