So, how likely is that? And who will it be?
Barring a surprise candidate who emerges in the next couple years -- not an impossibility by any means -- we have a decent idea of the potential 2016 field. Here's where the heavyweight potential candidates stand now and where we think they'll go in the next few years.
* Marco Rubio: Rubio is actually further to the ideological left on gay marriage than his rhetoric would suggest.
"Just because I believe states should have the right to define marriage in a traditional way does not make me a bigot," he declared at this month's Conservative Political Action Conference. The "bigot" part is what got press -- but more notable is that he said states should be able to ban gay marriage, meaning the issue should be left to the states.
In an interview with BuzzFeed in February, Rubio likewise said he was "uncomfortable with a federal constitutional amendment on anything, particularly on that, because it steps on the rights of states to define marriage." That was essentially President Obama's position until last summer, and Hillary Clinton's position until last week.
But Rubio is conservative Catholic, and his personal views on gay marriage are unlikely to shift. As of 2011 he also supports the Defense of Marriage Act, which bars federal recognition of same-sex marriages conducted in states where such unions are legal.
* Rand Paul: If Rubio is further left that one might expect, the libertarian-minded Paul is further right -- at least rhetorically. When Obama came out in support of gay marriage last year, Paul told an audience of social conservatives that he didn't think the president's views "could get any gayer.” "I’m an old-fashioned traditionalist," the senator later told National Review. "I believe in the historic and religious definition of marriage."
At the same time, Paul suggests that the tax code and health insurance should be made neutral so that gay couples benefit from the same breaks as married ones. And like Rubio, he has said that gay marriage should be left to the states to decide. He said Sunday that he is okay with the government is "neutral" on gay marriage; in February he said he was "not sure" how he felt about DOMA.
Paul is already making moves in Iowa, where social conservatives are key; an embrace of gay marriage is unlikely. But he's already willing to let other states legalize gay marriage and to let gay couples have some federal benefits; he could expand that to mean marriage in all but name.
* Chris Christie: New Jersey Gov. Chris Christie (R) vetoed a bill legalizing same-sex marriage in the state, although he supports a statewide referendum on the issue. He has also agreed to strengthen the state's civil unions legislation, which still puts him to the left of many Republican officials. And he talks about gay rights in a way that's designed to appeal to supporters, not opponents. In 2011, before the president endorsed gay marriage, Christie declared that "my feet are firmly planted right next to President Obama" on the issue.
"While Governor Christie doesn't support marriage equality, he does have a good record," said Jimmy LaSalvia of the gay conservative group GOProud. "He also does a good job of talking about how he's thought about how issues affect gay people."
As a Roman Catholic -- and as someone who would have to work hard to earn conservatives' trust in a GOP primary -- Christie is not likely to be the first to step out with a personal endorsement of gay marriage. But he could well be the first to argue that his personal opinion doesn't mean gays shouldn't be allowed to marry.
* Jeb Bush: As on immigration, Bush's views on gay marriage are complicated. He believes in traditional marriage, but he supports recognition for gay couples.
“I don’t think people need to be discriminated against because they don’t share my belief on this, and if people love their children with all their heart and soul and that’s what they do and that’s how they organize their life that should be held up as examples for others to follow because we need it," he told Charlie Rose last June. "We desperately need it and that can take all sorts of forms. It doesn't have to take the one that I think should be sanctioned under the law." Likewise, he told the conservative CPAC conference earlier this month that "way too many people believe Republicans are ... anti-everything," including "anti-gay."
Back in 2006 Bush said he was leaning towards support for a constitutional ban on gay marriage in Florida, after previously holding that the ban was unnecessary. (Same-sex marriages were already illegal under state law). But in the gay marriage debate, six years is a long time. Like Christie, Bush seems positioned to move toward gay marriage support if he so chose.
* Paul Ryan: While his focus is on economic issues, Ryan has a consistent conservative record on gay marriage. He supports both the Defense of Marriage Act and a constitutional ban on gay marriage.
“The institution of marriage is an integral part of our civil society and its significance goes well beyond eligibility for benefits and similar considerations. Its future should not be left to a few overreaching judges or local officials to decide,” Ryan said in a 2004 statement. “That’s why I support this effort to amend our Constitution to protect marriage.” He has described himself as a "big supporter" of Wisconsin's 2006 constitutional amendment banning gay marriage. On the other hand, he did vote for the Employment Non-discrimination Act in 2007. Given how conservative he is now he could shift a bit and still be to the right of Rubio and Paul.
What's clear is that none of the top-tier candidates are likely to be the first movers on supporting gay marriage. More likely, a second or third-tier GOP candidate will be the first to embrace same-sex marriage, just as former Utah governor Jon Huntsman backed civil unions in the 2012 race. (Huntsman endorsed gay marriage early this year).
"There might be a Republican candidate who supports gay marriage, but there won't be a Republican president," said Tony Perkins, president of the evangelical Family Research Council. Should leading figures move too far on this issue, he warned, a third-party movement is possible: "The Republican Party may very well push the base out of party."