"I think we're going to have problems politically until we get some sort of third-party movement or some voice out there that can put forth new ideas," Huntsman told MSNBC Thursday.
"Gone are the days when the Republican Party used to put forth big, bold visionary stuff," Huntsman said.
"Someone's going to step up at some point and say we've had enough of this," he said.
The former Utah governor and ambassador to China dropped out of the presidential race Jan. 16 and endorsed Mitt Romney.
Asked about his endorsement, he said, "I'm not a surrogate for anybody."
"The real issues are not being addressed [by the Republican candidates] and it's time that we put forward an alternative vision, a bold thinking," he said. "We might not win, but we can certainly influence the debate."
When asked who the "we" referred to, he said, "a whole bunch of Americans out there that can't find a place politically."
But he quickly ruled out his own bid.
"That ain't gonna be me, by the way," Huntsman said. "I'm not interested in that."
Huntsman rejoined the private sector two weeks ago, joining the Ford Motor Co. board of directors. He succeeded his father two weeks earlier as chairman of the Huntsman Cancer Foundation.
But while he denied an interest in running, he placed second, behind presidential hopeful Rep. Ron Paul, R-Texas, in an online candidate-drafting process by Americans Elect, a non-partisan organization hosting the first national online presidential primary in May to put a third presidential contender on the ballot in all 50 states.
"All I can say is, I'm looking at the political marketplace and the duopoly is tired and we're stuck in a rut," Huntsman told MSNBC.
His comments followed a similar expression of dismay from former Republican Party Chairman and ex-Mississippi Gov. Haley Barbour, who told ABC News, "If the Republican primary voters continue to split up their votes in such a way that nobody is close to having a majority, then there is a chance that somebody else might get in."
Barbour, 64, said it would not be "necessarily bad" for a "white knight" candidate to emerge at the Republican National Convention in Tampa, Fla., the week of Aug. 27.
"Romney, [Rick] Santorum, Paul or [Newt] Gingrich -- I don't think any of them has made the case that 'I am the guy who has the best chance to beat Obama,'" said Barbour, party chairman from 1993 to 1997, during which time the Republicans captured both the House and Senate for the first time since 1954.
New Jersey Gov. Chris Christie and former Florida Gov. Jeb Bush, a younger brother of former President George W. Bush, are often suggested as candidates who might unify the party after a bruising and divisive race.
Christie, who has endorsed Romney, said he still faced pressure to wage his own campaign.
Jeb Bush, who has not endorsed anyone, had no immediate comment about running, but said in Dallas Thursday he watched the debates and found it "a little troubling sometimes when people are appealing to people's fears and emotion rather than trying to get them to look over the horizon for a broader perspective."
"I think it changes when we get to the general election," Bush said. "I hope."
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