There's the first problem right there. People getting by on minwage jobs do not work 80 hours every 2 weeks. They work 80hrs every week. Minimum. I knew a guy, a Thai immigrant, who worked a day job, a night job, and a weekend job. So double that to over $1800/mo. Yeah, you can get by on that.
Second, the number of heads of households who work min wage jobs is miniscule. Holders of such jobs are typically married women returning to the workforce, teenagers, people living with others who are earning money.
Finally, very few people stay at min wage. As they develop skills and experience they increase their pay scales dramatically.
Of course if you increase the min wage you do away with jobs like that, and make it harder for people to get on the ladder. This is why black teen unemployment is over 40%.
That isn't entirely true, at least in my personal experience. Every job I've had that I was paid hourly my employer would not allow me to work more than 40 hours a week because they did not want to pay overtime.
This is yet another unintended consequence of government interference. Some people, myself many times, would be willing to work past that 40 hours a week and forgo getting paid that time and a half--but that is too bad. I was limited by government regulation on the possible money that I could get paid per pay period.
Employers will always do what they have to to cut costs, and if that means bringing in additional workers and cut hours to prevent them from going into overtime they will.