Greg Sargent believes so:

Whatever you think of Media Matters, there’s no denying that the group led a campaign against Dobbs that had to have played some kind of role in his departure. CNN president Jonathan Klein reportedly told Dobbs months ago that he wanted Dobbs to tone down his opinions. It’s hard to imagine that the constant drumbeat of attention paid by Media Matters, Think Progress, HuffPo, TPM and other sites to Dobbs’ more outlandish opinions — and the damage they were doing to CNN’s news brand — didn’t put Klein and CNN on edge.

There has been a vigorous campaign from the blogosphere to get CNN to dump Dobbs. Given the fact that Dobbs up and quit with no warning in the middle of his contract implies that CNN was rather willing to let him go. I wouldn’t doubt if the rapid decline of CNN ratings coupled with outside pressure contributed to CNN agreeing to his departure so easily.