Public support for same-sex marriage has been rising dramatically. Yet a big majority of Republicans oppose it. And they tend to nominate candidates for Congress and the presidency who are out of step with the shift in public opinion, at least at the national level.
Republicans will confront this issue in congressional and governors' races next year. It could play an even bigger role in the 2016 presidential election. Anyone supporting same-sex marriage would face tough resistance in GOP primaries, which conservatives dominate.
The more attention the issue gets, the more it might alienate much-needed independent voters in the general election.
"Many of us in the Republican Party would like to see this issue go away," said Mark Graul, a Wisconsin political strategist. Still, he said, same-sex marriage is a less important issue than it has been portrayed, and relatively small numbers of voters consider it their top priority.
Cheney, the former vice president, is trying to limit the political damage to his daughter Liz, who wants to oust three-term GOP Sen. Mike Enzi in next year's Wyoming primary. Liz's sister, Mary Cheney, is married to her long-time companion, Heather Poe.
The two sisters began a highly public quarrel Sunday when Liz Cheney told Fox News Sunday she opposes legalized same-sex marriage, but the issue should be left to the states. Mary Cheney wrote on Facebook: "'Liz -- this isn't just an issue on which we disagree, you're just wrong -- and on the wrong side of history."
Poe went farther. She wrote that Liz Cheney had always supported the lesbian couple and their two children, and "to have her say she doesn't support our right to marry is offensive."
Dick Cheney and his wife, Lynne, tried to calm things on Monday. They said their daughters love each other, but "Liz has always believed in the traditional definition of marriage."
In 2009, Liz Cheney told MSNBC she would oppose a constitutional amendment to ban same-sex marriage in every state. Then, as now, she said states should decide how to deal with same-sex marriage. Fourteen states and the District of Columbia have legalized it.
Gallup polls have found substantially higher support for same-sex marriage since 1996, especially among young adults and non-Republicans. In July, 54 percent of Americans said same-sex marriage should be legal, compared with 27 percent in 1996.
Support is much higher among people aged 18 to 29.
Most of the increase was among Democrats and political independents. In July, 28 percent of Republicans supported legalized same-sex marriage, compared with 16 percent in 1996. Among Democrats, support is now 73 percent.
The 2012 Republican Party platform reaffirmed "our support for a Constitutional amendment defining marriage as the union of one man and one woman." Mitt Romney, the presidential nominee, says he still holds that view.
Many Republicans, however, consider it a losing battle. Nearly three-quarters of Republicans told Pew Research that recognition of same-sex marriage is inevitable.
Some prominent Republicans say the party can embrace the trend without sacrificing conservative values. "What could be more conservative than support for more freedom and less government?" former GOP national chairman Ken Mehlman, who in 2010 announced he is gay, wrote in The Wall Street Journal last year. "And what freedom is more basic than the right to marry the person you love?"
Many conservative groups, however, remain strongly opposed. If same-sex marriage is legalized, "taxpayers, consumer and businesses would be forced to subsidize homosexual relationships," says the Family Research Council, which is influential in some Republican primaries.
Some Republicans seek a middle ground.
After Romney's loss, previous rival Newt Gingrich suggested Republicans oppose same-sex weddings in churches but allow "a legal document issued by the state."
"I think that this will be much more difficult than immigration for conservatism to come to grips with," Gingrich told The Huffington Post. "The momentum is clearly now in the direction in finding some way to accommodate and deal with reality."
Several elected Republicans said Tuesday they believe other issues will overwhelm same-sex marriage in coming elections.
"The electorate is a lot more focused on the rising cost of health care, the diminished benefits they're getting, plus the economy and national security issues than they are about that particular issue," said Sen. Saxby Chambliss, R-Ga., who is retiring.
New Jersey Gov. Chris Christie proved this month that a Republican official can thrive - in some states, anyway - by officially opposing same-sex marriage but saying he will do nothing to block it. In exit polls following his landslide re-election, only 6 percent of New Jersey voters said same-sex marriage was their top issue. Sixty percent of all voters said the state should legalize same-sex marriage, and half of them backed Christie.
In solidly Republican Wyoming, Enzi says he has always supported a constitutional ban on same-sex marriage. Since that's a more rigid stance than Liz Cheney takes, will it become an issue in their primary?
"I'm not going to make it one," Enzi said Tuesday.