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Mr. Innis, who, like Mr. Tisei, is legally married to a man, predicted that by the 2020 presidential election, the national party platform would be more welcoming to same-sex marriage. Mr. Tisei said it would be wise for that to happen. And Mr. DeMaio said, “I could care less about the party platform.”

“I think our base actually has moved, and it is the party leaders and elected officials who are afraid of their shadow who haven’t caught up to that,” Mr. DeMaio said, adding that Democrats and gay-rights groups that have benefited from the battle are scared of the idea of Republicans moving on social issues.

“They are looking at it saying, ‘How do we continue this cash cow?’ and Democrats are trying to figure out how they [can] continue to use this as a wedge issue to drive out their base,” he said. “Democrats are terrified about this happening.”

An ABC News/Washington Post poll released in June showed that 56 percent of Americans support allowing persons to marry someone of the same sex, compared to 38 percent who are opposed.

The support differed along partisan lines, with 67 percent of Democrats, 58 percent of political independents and 37 percent of Republicans supporting it. The issue also divides generations, with 77 percent of adults under age 30 supporting it, compared to just 38 percent of seniors.

Legally, the issue also is trending toward gay marriage.

Since the 2012 presidential election, the Supreme Court has struck down DOMA as unconstitutional and cleared the way for California to resume offering marriage licenses to gay couples. According to Lambda Legal, there have been 25 rulings in favor of same-sex marriage. Gay marriages now are performed in 19 states and Washington, D.C.

The court rulings have outraged some social conservatives, who say federal judges have substituted their own ideology for the right of the people to define marriage “as it has always been defined.”

But Mr. Tisei said the issue is similar to that of interracial marriage and predicted an eventual landmark Supreme Court ruling such as the Loving v. Virginia decision that invalidated laws barring interracial marriage.

“The principle is simple: Should everyone be treated equally and fairly under the law?” Mr. Tisei said.

Mr. DeMaio said it’s not about imposing a viewpoint but about protecting equality.

“If you don’t support gay marriage, don’t get gay married,” he said, but added, “If someone in government tries to get you to recognize or perform a gay wedding, I will be at the front of the pack to defend your right.”