This a favorite answer - get the money from the rich, greedy corporations.
The problem is, when you pass a minimum wage law you pass it for everyone and the majority of people in this country don't work for a rich corporation making record profits.
And here's the irony - the small businesses can't handle the increases in labor costs, but the big corporations CAN. So a local hardware store (for example) can't raise their prices to cover their costs because Home Depot can afford to keep them low. The end result is the small business goes out of business or lays people off. To be fair - this isn't bad for the workers - they can go work at Home Depot. But if you don't like big corporations, you shouldn't be so quick to promote ideas that cost everyone money.
Another issue that exists with fast-food places (where many of these minimum wage jobs exist) is that they use the franchise model. Meaning - every McDonalds isn't owned by McDonalds - it's owned by a local person or small company and they just pay fees to McDonalds. This means that a single store doing poorly can't be held up by the profits in another city - they're owned by different people.