“What we have really seen is the inability of either party to reach across the aisle, as we used to, and reach a meeting of the minds,” Boren said. “The most important ability the next president must have is to really bring the two parties together and make the two-party system work again in a way that it did 20 or 25 years ago.”

The organization has set up an online nominating process in which registered voters can draft candidates, who then would be required to pick opposite-party running mates ahead of a June "primary" open to registered voters across the country. According to the Times, the group has secured a place on the ballot in 16 states, with enough signatures already collected in 13 others.

Boren backed President Obama in the 2008 election, and said he might do so again — despite his support for the group.

“If Americans Elect produces a ticket that is not well-qualified, that I don’t think has the strength to bring the country together, it’s certainly possible that I would support President Obama’s reelection,” Boren said.

The group has millions from supporters backing its efforts, but two of its leading "nominees" as of earlier this month were late night comedian Stephen Colbert and Republican presidential candidate Ron Paul, who signaled that he isn't interested in a third-party run. That's cast doubt on how effective the group's campaign will actually be.

Other leading candidates include Sen. Bernie SandersBernard (Bernie) SandersDems ponder gender politics of 2020 nominee 2020 Dem contenders travel to key primary states After Florida school shooting, vows for change but no clear path forward MORE (I-Vt.) and Jon Huntsman, who dropped out of the GOP race earlier this year after a poor showing in New Hampshire. Huntsman suggested last week that a third party would be a good development in American politics, although he said he wasn't interested in running as an outside candidate. 

"I see zero evidence of people getting out there and addressing the economic deficit — which is a national-security problem, for heaven's sake," he said on MSNBC. “I think we're going to have problems politically until we get some sort of third-party movement or some alternative voice out there that can put forward new ideas."