At the outset of the 2004 presidential primaries, Howard Dean was considered a far-out radical, in large part because as Vermont governor he had signed a bill providing civil unions for gay couples. By the end of the election, however, all the Democratic candidates had come out in support of civil unions, and even George W. Bush said that if a state chose to have them, that was fine with him. Four years later, not much had changed. The leading Democratic candidates all said they supported civil unions, but still thought marriage should be between a man and a woman.
And Barack Obama has held to that standard, despite saying his views on marriage equality are "evolving." People on both the left and right take this to mean that he believes in marriage equality, but doesn't yet have the political courage to come out and say so publicly. His message to the gay community has essentially been: "Look, I repealed 'Don't Ask, Don't Tell,' and my administration isn't defending the Defense of Marriage Act in court, and on gay marriage, well, just be patient." The First Lady has implied that future Obama Supreme Court nominees will support marriage equality. But nobody really expects the President to do a public shift before election day. The gay community is, if not satisfied, then accepting of where he is, and Obama is too cautious to risk alienating independent voters (though whether he would is debatable). Nevertheless, I'm pretty sure that Obama will be the last Democratic president who didn't support marriage equality.
The Democratic field for the 2016 nomination won't be clear until about November 7, the day after Obama's re-election campaign succeeds or fails. There are a few likely candidates, however. Two Northeastern governors—Andrew Cuomo of New York and Martin O'Malley of Maryland—are almost certain to run, and both of them successfully pushed through marriage equality laws. If Hillary Clinton decides to run, you can bet she'll have a dramatic announcement of her own evolution on the issue (she hasn't officially changed her position yet, though she did come out in support of New York's law). Some have suggested that if she wins a Massachusetts Senate seat, Elizabeth Warren could run for president four years later; she supports marriage equality. Chicago mayor Rahm Emanuel is thought to harbor presidential ambitions; he too is a supporter. The only frequently mentioned potential 2016 candidate I can think of who doesn't support marriage equality is former Virginia governor and current Senate candidate Tim Kaine.
While Democrats don't have nearly as many litmus tests as Republicans do, this is almost certain to be something that is expected of anyone who wants to be the party's nominee in four years, and forever after. The really interesting question, though, is how long it takes to get a Republican presidential nominee who supports marriage equality. I'm going to guess it'll be 2024.