I really love the classic film of Steinbeck's Grapes of Wrath, so made a point a couple years ago to read the book, which I also greatly enjoyed. One of the things that really struck me was how the prevailing wages for rough physical work that the family encounters actually falls basically below the point of being able to even afford adequate caloric intake to maintain that level of effort over time. In one sequence the whole family works the whole day picking fruit at some farm, and the wages they're paid don't even buy a big enough meal to feed them all to satisfaction. The next day they find the wages are even being cut further. People were working for less money than it costs just to survive.
Now, you can say it's just a book, but I see no reason to doubt that this happens in extreme economic conditions, and Steinbeck was basing his work on actual visits he made to the Hoovervilles and camps these migrant workers created (which were actually worse than he portrays in the book; people really were starving to death).
There's plenty of room for debate about where the minimum wage should be set, but even if it was true that the minimum wage "costs jobs" I wouldn't be persuaded against its necessity in the face of the above. Desperate people will work for near anything, and if a job's "marginal utility" is such that it pays less than survival wages, the worker is better off if that job doesn't exist. Fortunately the empirical evidence is that the Econ 101 theory which says minimum wages kill low wage jobs is just flat false.