If Obamacare reduces labor supply, will it raise wages?
That sounds like reasonable, textbook economics. But I don't think it is true. The problem is that the logic is entirely partial equilibrium. It is holding everything else constant. But that is surely not right in the long run. Lower labor supply means lower income, which means lower saving, which means lower investment, which means a lower capital stock, which means lower productivity, which means lower labor demand.
Perhaps the easiest way to think about this issue is in the context of a Solow growth model. In the Solow model, the steady-state real wage is a function of technology, the saving rate, and the population growth rate. If labor supply per person suddenly falls by, say, 2 percent and stays there, the real wage will rise initally, but it will eventually return to its former level. Steady-state income per person falls by the full 2 percent.
One effect that might occur is a change in the composition of labor income. If the Act reduces labor supply primarily among the low-skilled, while not having that effect among the highly-skilled, then we might get a change in the relative wages of skilled and unskilled. But an overall increase in real wages seems unlikely.