By popular demand, I will contribute my two cents.
A minimum wage creates unemployment if we assume:
1. The market is perfectly competitive.
2. The minimum wage is set above the equilibrium value.
It's pretty easy to assume that raising the minimum wage would create unemployment based on our classical teachings, right? Well, as the current crisis clearly shows, the real world is not a perfect, simplified model. Some empirical studies have shown this to be the case.
As a note, I don't have references to those case studies anymore or feel like looking them up, but I'm sure someone could find one of them if they didn't trust my word.
Anyway, there are likely to be distortions in our "perfect" market. From the evidence, it appears that many business that pay minimum wage (say, grocery stores) actually act with some monopsony power.
In a monopoly, the seller controls how much product will be sold. In a monopsony, the buyer controls how much product will go through the market. In many cases, such as instances where transportation costs are too high to allow for perfectly fluid markets or where information is asymmetric, these businesses might be able control the wages of their employees without competitors driving them up to a competitive equilibrium.
Thus, if we can set a minimum wage at the point where the competitive wage would be, we can actually remove the dead-weight loss created by the real world imperfections to the model.
The studies I've alluded to have shown that raising the minimum wage have had insignificant effects on the unemployment rates. Of course, there are probably others that show otherwise. From my experience with studying economics, the real-world results seem inconclusive.
The minimum wage would never be the answer to eliminate poverty, but it can safeguard against wage discrimination in monopsonistic economies, which can and do exist. Though it would not eliminate poverty, it can curtail it. Unless we would like to live in a country with utter destitution...
Get the point?