I would stress that it is the very long run results that matter, once all lock-in and morale effects are gone or redrawn and the eventually-old legislated minimum wage is simply a relative price like any other. But what about the short run? Timothy Taylor has a good survey of a recent study (pdf), and here is his concluding paragraph:
I’m willing to let the evidence tell me the story, and on many economic issues, it takes time for the evidence to accumulate. As more cities raise minimum wage, the picture will clarify. But the early evidence from Seattle is that a higher minimum wage at the city level doesn’t raise total earnings by much, because low-skilled workers end up with fewer hours on the job.
There are many other points at the link.