When I was working minimum wage there was also the working poor: they needed every penny. If they called in sick you knew they were sick. If you asked them to work overtime they did their best to take it because the extra money was needed (they often couldn't find a sitter on short notice though). They didn't stay in minimum wage for long, their efforts were noticed and they were offered promotions to management (not all accepted because management often meant moving away from family, but in that case they still got maximum raises until they reached the top of the pay scale).
Note that many of the working poor got themselves into that position because of their choices, generally they had a kid at 16 and dropped out of school as a result (at best finished at the bottom of their class). They were failing to dig themselves out of the hole of their bad life choices because that kid takes the time needed to get a better education. In short they lack moral fortitude in that they were (and are...) sleeping around, but not in that they are not working hard for their employer.