For one thing, given her disastrous experience with health care reform in 1993-1994, it's reasonable to assume that she would have stayed away from that issue at all costs.Jonathan Chait basically agrees; Kevin Drum dissents.
I'm with Drum, and not just for his excellent reasons. The fallacy here, I think, is the idea that presidential preferences on issues of public policy are the critical input into what presidents actually do. Not so! Presidents are driven by all sorts of things: events; the president's skills; his or her personality; historical constraints; or, most relevant here, party and the nomination process. The evidence is overwhelming that it was impossible to win the Democratic nomination for president in 2008 without making health care reform a first-tier platform item, and once that was the case any possible nominee would have moved strongly ahead with a plan, really at about the same time Obama did. The nominating coalition, not to mention the nominating coalitions responsible for the elections of most Democratic Members of Congress, demanded it. That's easy to see from the actual platforms of the candidates; they all pushed health care to the top of their agendas. And once a reform effort was underway, the logic of the situation called for persevering as long as victory was plausible.
Now, it's possible that Hillary Clinton would have failed where Obama succeeded. We can't know how adept she would have been at handling the presidency. Perhaps she would have failed to win support of the necessary GOP votes in the Senate for the stimulus, and perhaps that would have killed off the health care effort. Perhaps she would have been considerably less popular than Obama, whose approval ratings have held up fairly well in the face of tough economic times, and that would have killed off health care reform. But those are skills arguments, not arguments about her policy preferences, and of course one can argue that she would have been more, not less, skilled, and therefore passed health care reform more easily (and perhaps even with a public option and other provisions conservatives dislike). I tend to think that she would have been somewhat less adept than Obama, but that's obviously speculative. Guesses about their true policy preferences (or lack thereof) is speculative too, but in my opinion basically irrelevant. Obama, Clinton, Edwards, Bill Richardson or Joe Biden, no candidate was going to win the 2008 nomination without making health care reform a top priority and acting accordingly in 2009.