Hillary Clinton came second in the nomination fight of 2008. If she were a Republican, that would make her a near-certainty to be nominated in 2016. Five of the past six Republican nominees had finished second in the previous round of primaries. (The sixth was George W. Bush, son of the most recent Republican president.)I've written about this before several times (most recently here), but it's just not a very useful comparison. Republicans simply have happened to have had far more cycles with fairly obvious nominees than have Democrats. We don't know how a Democrat with a profile similar to Bob Dole's in 1976 would have done, because we just haven't really had any, for a variety of reasons.
Democrats, by contrast, prefer newcomers. Six of their eight nominees since 1972 had never sought national office before.
Put it this way: on the one hand, the 2012 cycle sort of confirmed the "next in line" theory...if, that is, we conclude that Mitt Romney was the runner-up in 2008, which is sort of true but also sort of not true (by some measures, the Huck had a better argument for having come in second). But at the same time: does anyone really think that Rick Santorum will be an easy winner in 2016? If we don't think so, then we clearly don't believe that finishing second has any magic power; we might, for example, think that George H.W. Bush's vice-presidency was far more important in 1988 than were his 1980 primary wins. And once we loosen the definition of "next in line" to simply mean the most logical nominee of those who make it to Iowa (or something like that), then we find that Democrats are pretty much just as likely to select that candidates as are Republicans.
(Okay, minor nitpick on the count, too, those "six" nominees who "had never sought national office before." Assuming we're ignoring renominations of sitting presidents, I count McGovern, Mondale, and Gore as having previously sought national office, while Carter, Dukakis, Clinton, Kerry, and Obama had not. Even if Mondale's quickly aborted presidential run doesn't count, which I'm fine with, surely the vice-presidency is a national office).
The big Republican win for next-in-line is John McCain, who had very little going for him other than having been the runner-up in 2000. But there's not much more to it, really.