It is possible to finish your dissertation and blog at the same time!!! Even more evidence of this in the comments over at Crooked Timber. Very encouraging news.
Actually, I think the blogging actually helps. For one thing, I think writing a little bit every day helps my writing. For another, it keeps me from going crazy just thinking about the dissertation all the time. And sometimes (although rarely), it actually helps me think about issues that directly relate to my thesis.