"So what did the two most important people in this country sit down and talk about yesterday at lunch?” Huntsman asked. “When everything else is done, and the election is wrapped up, it isn’t about social issues. It isn’t about the fringe issues. They sat down and talked about America’s leadership in the world."

Huntsman went on to warn that the party was occasionally consumed by such "fringe issues, and it gets us stuck in the alleyways of life that take our focus away from what is really important for the American people, and that is individual freedom and that is getting the budgets balanced so people can get on with their lives.”

Huntsman, who was the former U.S. Ambassador to China under President Obama, also urged Republicans to cool their rhetoric surrounding the terrorist attack in Benghazi.

"What I'm saying about the Benghazi incident is let's lower the politics," Huntsman said. "Let's let the experts collect the information."

He also downplayed any suggestion that he could serve as Secretary of State, with Hillary ClintonHillary Diane Rodham ClintonBiden slams Trump over golf gif hitting Clinton Overnight Cybersecurity: Equifax hit by earlier hack | What to know about Kaspersky controversy | Officials review EU-US privacy pact Overnight Tech: Equifax hit by earlier undisclosed hack | Facebook takes heat over Russian ads | Alt-right Twitter rival may lose domain MORE planning to leave the job at the end of the president's first term — although seemingly indicated he would accept the job, if asked.

"I don't play the hypothetical game," Huntsman said. "We have moved on. My history has always spoken to putting my country first, and if I didn't, my two sons at the U.S. Naval Academy would never forgive me. The president will choose who he wants, and it serves no purpose playing the speculation game."