It depends on how you define "work". Apparently only 6% of first-time homebuyers cited the tax credit as the driver behind their purchasing decision. I suppose that's plausible, given low, low interest rates--which are a far greater contributor to affordability. But I'd be surprised if a majority didn't factor the tax credit into the price they paid . . . which itself could have helped the market clear in a lot of places. If your goal was to inject purchasing power into the economy, and help unlock the housing market, I suppose it worked, at least somewhat. If your goal was to help people afford houses, less so.
"Do not touch the water. There is nothing more irradiated than the water itself."