As the run-up to the general election intensifies, same-sex marriage offers the parties one of their sharpest contrasts. But in a reversal of strategy from eight years ago, when President George W. Bush’s reelection team seized on the issue to energize his party’s social conservative base and win over some swing voters opposed to gay marriage, the Republicans of 2012 are so far treating the issue gingerly.

In the 24 hours since President Obama announced his support for gay marriage and turned it into a hot-button campaign issue, presidential candidate Mitt Romney and other Republican leaders have chosen their words carefully.

Romney reaffirmed his opposition to gay marriage. “I believe that marriage has been defined the same way for literally thousands of years by virtually every civilization in history and that marriage is by its definition a relationship between a man and woman,” Romney said Thursday on Fox News. But he added that same-sex couples should have the right to adopt children and start families, adding that the marriage issue was “tender and sensitive.”

Those sensitivities reach deep into Romney’s coalition. Some top Republicans described a growing divide within the GOP, with most of the party’s elected leaders in step with the social conservative base by publicly opposing same-sex marriage but softening their tone to avoid alienating the moderate middle.

Some of Romney’s biggest financial backers — including Lewis M. Eisenberg, a former Republican National Committee finance chairman, and hedge fund managers Paul Singer and Daniel S. Loeb — have become public advocates for gay marriage, as have other Romney supporters, including former vice president Dick Cheney and former ambassador to the United Nations John Bolton.

Behind the scenes, influential donors and top strategists are counseling Republican candidates to avoid hot rhetoric or stigmatizing gay people, fearing a potential backlash from voters, who, polling suggests, are fast growing more open to gay marriage.

Steve Schmidt, a strategist for John McCain’s 2008 campaign as well as Bush’s campaigns, said Obama’s announcement Wednesday drew attention to “deep division” within the GOP on the issue.

“This really spotlights a fissure in the Republican Party between the southern evangelical wing of the party — where they don’t mind government intrusion into the bedroom and into individuals’ private space — and the limited-government side of the party,” Schmidt said. “Looking back at this from 50 years in the future, people who are on the wrong side of this issue aren’t going to stand very well in history’s light.”

Ed Gillespie, a senior Romney adviser, said Thursday on MSNBC that gay marriage would be a campaign issue because “it engenders strong feelings on both sides.” But, he added, “it’s important to be, you know, respectful in how we talk about our differences.”

On the campaign trail Thursday in Nebraska, Romney didn’t talk about those differences at all. Although the issue could help unite social conservatives behind his candidacy, Republican strategists said they see it as a distraction from Romney’s core message on the economy, the issue on which they believe he can beat Obama.

“I don’t think Romney wants to talk about gay marriage,” said Mark McKinnon, a media strategist on Bush’s campaigns. “Every day spent talking about it is a day lost talking about the economy. Focusing on this issue does not help Republicans with the independents who are the key to winning.”

It is a delicate gamble for Romney, who has struggled to earn the trust of many of the evangelicals who make up the party’s conservative base and oppose gay marriage. Romney’s advisers assume they will not expect him to sound a call to arms.

“Everyone’s going to debate whether he talks about it frequently enough and loudly enough, but it doesn’t change his position,” said Mark DeMoss, a senior adviser to Romney and liaison to the evangelical community. “The governor’s position on it is well known regardless of how loudly he says it.”

With both houses of Congress as well as the White House at stake this fall, Republican leaders on Capitol Hill have taken an approach similar to Romney’s.

Asked during a news conference Thursday about gay marriage, House Speaker John A. Boehner (Ohio) said, “I believe that marriage is the union of one man and one woman.”

But Boehner made clear that he had no desire to discuss the issue any further. “The president and the Democrats can talk about all this all they want,” he said, “but the fact is the American people are focused on our economy and they’re asking the question, ‘Where are the jobs?’ ”

GOP pollster Whit Ayres, who has advised candidates coast to coast, said Republican candidates need to have a clear stand on what they believe about gay marriage — and then spend “95 percent” of their time talking about other issues.

“They need to spend their time talking about how we’ll turn around this horrible economy and get people jobs and health care and improve our educational system and stop this spending spree that’s pushing us to the brink of bankruptcy,” Ayres said.

That is a shift from Republican strategy in 2004, when Bush’s allies organized gay-marriage ballot measures in 11 states, designed in part to help turn out social conservative voters.

Now, more than 30 states have passed gay-marriage bans, including North Carolina, whose voters this week approved a constitutional ban.

But polling shows sentiments are shifting. A Washington Post-ABC News poll in March found that 52 percent said gay marriage should be legal, while 43 percent said it should be illegal. Among Republicans, 57 percent opposed same-sex marriage, and 39 percent favored it.

GOP strategist John Weaver warned that Republicans will be “long-term losers” if they don’t soften their strident opposition to gay marriage.

“I think you’ve seen a muted response from some of our leadership, who I think get that,” Weaver said. “Not saying anything is progress from where we were in 2004, when we were basing a presidential campaign in large parts on some of these efforts. I hate to say that a mute voice is progress, but it is.”