The distinction becomes particularly clear when you consider societies of one-- e.g. a castaway. If he wasn't industrious enough, a castaway could clearly work in a way that wouldn't guarantee sufficient food and shelter. Ergo it is possible for work to generate less wealth (= be worth less) than would guarantee food and shelter.
I think what you mean to say is that if people can't generate enough wealth to cover certain minimum requirements, the rest of us should make up the difference. And I don't think anyone would argue with that general principle.
Sources: I lived on < $10,000/yr for quite a while.
It should be noted that I am not advocating reducing (or increasing) minimum wage. I think that the issue that people try to address via minimum wage is a clusterfuck of an issue that won't really be solved without a pretty large paradigm shift in how people acquire, or are provided with, their food and shelter.
$22.50/day or $8,218.13 per year in expenses. At $5/hr, you are making $10k a year for a full time job w/ 2 weeks vacation.
FYI a single ride on the bus/light rail in the Bay Area (VTA) costs $3.75.