Asked whether he could support a Republican presidential candidate someday who supported same-sex marriage on NBC's "Meet the Press," he replied, "I think that's inevitable. There will be one, and that I think he'll receive Republican support, or she will. I think that … the answer is yes."

But Flake suggested that he will not be that candidate.

"I believe that marriage should be between a man and a woman. I still hold to the traditional definition of marriage," he said.

Mitt Romney, the party's 2012 presidential candidate, stated his opposition to same-sex marriage but said states could extend some rights to same-sex partners.

Ed Gillespie, a senior adviser to Romney's campaign, noted the GOP "platform right now calls for a federal constitutional amendment to ban" same-sex marriage.

"There may be a debate about that," he said, adding, "I don't think you would ever see the Republican Party platform saying we are in favor of same sex marriage."

The party, he said on "Fox News Sunday," has not been effective in communicating its position on the issue.

"I do think that in the context of this debate, as in so many other debates, Republicans have been cast in the negative … to say we are opposing something, as opposed to talking about what most Republicans are for," he said. “Most Republicans are also for the benefits of marriage in the legal system that are afforded, the protections like, for example, … hospital visitation rights or survivorship benefits, and I think you will hear more Republicans making that point, that we can do those things without having the government sanction same-sex marriage."

Support for same-sex marriage is significantly higher in the Democratic Party than the Republican Party. The mid-March CNN/ORC poll found that 70% of Democrats supported same sex-marriage and 25% of Republicans supported the same. Among independents, 55% supported same-sex marriage.