I don't know the answer to this, but I suspect that Bartlett is correct in general. I don't think he's specifically right about health care, which always seemed to be the issue she cared about most, but I don't really think you would have seen a lot of the successes that Obama has had under Clinton. I highly doubt that, for example, Clinton would have made any of the same moves Obama has to tamp down the drug war. Coming of age politically when she did, I doubt she would have touched that. I doubt even more that Clinton would have pursued an ambitious arms control treaty as Obama has. As for foreign policy, I think Obama's approach has generally yielded good results, perhaps better than a Clinton Administration would have, though one can never be sure. A Clinton Administration would undoubtedly have pursued different priorities--a stronger emphasis on women's rights around the world, probably less of an emphasis on Israel-Palestine considering Bill Clinton's disappointment in 2000, and in general probably the same broad contours with respect to Iraq and Af-Pak. That might have been good! Or not. Honestly, Obama hasn't really done too many out-of-the-mainstream things on foreign policy, and it's easy to imagine Clinton ordering many of the same actions.
There have been some disappointments for me over the past year or so, and a few blunders as well. But I still think the right guy won, and his record has been such that I'm happy with his performance so far--and the ways in which I'm unhappy with it (mostly security and civil liberties stuff) certainly weren't going to be any better with Clinton or McCain in command.