Looks like a great NPR Fresh Air, featuring Nate Persily.  A choice quote:

Nate Persily: “We don’t know for sure whether that’s going to be true. It’s true if you look at the non-ID population that is over-represented among racial minorities, and that has been shown in Texas and Pennsylvania and elsewhere. But again, some of those people would not have voted anyway, so it’s difficult empirically to say what share of the likely voter population would not vote as a result of a voter ID law.

“Nevertheless, if what we’re trying to answer is whether this law has a disparate impact in that it’s going to maybe deter minority voters at a greater rate than non-minority voters, then yes, I think you can see that effect. The partisan effects, it’s really hard to figure out. In Indiana, they had a voter ID law in effect when Barack Obama won that state in the 2008 election and black turnout actually went up. Of course, the fact that black turnout went up had a lot to do with him being on the ballot, so maybe if there hadn’t been a voter ID law, then we would have had a greater number of African-Americans that were turning out in that race anyway, but it’s very difficult to say exactly what the partisan and racial disparate impact is going to be.”