Most people who argue against the minimum wage assume labor demand is elastic, meaning the amount demanded will disproportionately change relative to price changes.  Here's a simply supply and demand chart to illustrate:
In the above chart, the government increases wages from P to P1 and demand drops from Q1-Q2.  In this example, the line Q1-Q2 is longer than P-P1, meaning the increase in price had a large impact on demand.
     However, what if demand is inelastic?  In that case, we'd be looking at the following chart:
Above we see the quantity demanded decrease slightly relative to the larger increase in price.  This means that even if wages increase, we still demand a certain amount of labor.
     The second chart is actually far more realistic.  Consider the following fact pattern: a store currently has 100 employees.  Because they're a profit maximizing entity, they are already using the optimal amount of labor (give or take say 5-7 employees).  Let's assume they cut their workforce by 25% because of the increased wages they must now charge.  At this level of cuts they'll see shelves stocked less frequently, fewer employees helping customers finding items and longer check-out lines. This will actually decrease their sales; customers will get tired of not being helped and will become frustrated with the longer lines.     
     The underlying reasoning is based on the production function, another basic micro-econ concept:
The horizontal line shows the total amount of labor while the vertical lines shows total output.  Notice that as L decreases, so does output.
      Anyway, food for thought. 
      Thanks to Jared Bernstein for first pointing this out awhile ago. 
[UPDATE]: Alan Kreuger's research confirms.
    



 
