Punishing industries built on unskilled labor is my problem. It makes more sense to place the burden of welfare on the whole economy, via taxes, since the government is the only entity in the position to redistribute wealth.
In my vision, the government would supply the first $X of everyone's wage, and pays for it by increases in income tax. This gives a huge stimulus to unskilled industries founded on a large number of laborers. Now instead of having to pay everyone a minimum of $7.25/hour, they pay $7.25 - X.
I don't think we have to set X at $7.25. That would be no good as many industries would get free labor, and people would be hired on the government dime to just sit around and do nothing for 40 hours a week. Someone smarter in economics than myself would figure out X, but perhaps it would be something like $5/hour.
"Wouldn't Walmart and McDonald's just set their wage to $0 anyway, and make workers suffer with $5/hour? Isn't that going backwards?"
No, they would soon find themselves in a position of needing to compete for unskilled labor. (Whoa, the thought!) So they would add some wage on top of the government subsidy, and that would settle at a natural competitive level. That might be $4/hour or whatever as it fits their business model.
And X would adjust as needed over time to balance the economy.