I could survive just fine off a full-time minimum wage job in my state of Michigan. That's 9.45/hour or about $1500/month. I rent a pretty nice place in a college town for $550/month (across the street from campus, middle of downtown, utilities included). I eat mostly pasta and canned soup, but that's just because it's easy and cheap, and I do go out to eat with my girlfriend once or twice a week. let's say another $700/month for money, phone bill, gas, and walking-around money. Just to round it out let's add $200/month to put into saving for unexpected expenses and $100/month for car insurance or anything else I forgot.
I'm on my parent's health insurance, I think if that were not an option it would really complicate things. Google says the average annual health insurance premium is $15,500, which would basically be my entire yearly pay. I think when you work more than 30 hours your employer is supposed to pay some of that, and maybe there's subsidies too for people on low income, I'm not really sure how it works.
So basically, the current minimum wage is fine for me. For a single parent with 3 kids, it would obviously not be nearly enough. But also, I'm not sure I'm capable of doing any work that's worth a living wage for a single parent with 3 kids, so raising the minimum wage that high would probably put me out of a job. Maybe the minimum wage should be set as high as it can be without costing too many jobs, then the government should give everyone the support they need to feed their families and not be homeless.