But Roemer objected, saying Americans eventually voted based on self-interest.

"I think it's always a component part — how do you look, how do you act, do you make me laugh? — that's always a part of it. But at the end of the day, Americans always vote in their family's best interest. At the end of the day, American has demonstrated the ability to choose between Abraham Lincoln and the other guy. Look, Donny, don't trivialize it," Roemer said.

The exchange came as part of a larger critique of the American political system provided by Roemer. The former governor blasted President Obama for only now proposing tax reform.

"We have a code that's not fair. We have a code that's not growing America. So you would think the president would make it a top priority, wouldn't you, if we need jobs? He just proposed tax reform after three years in office. It's not a priority because it's a money-raiser for Congress," Roemer said.

Roemer originally sought the Republican presidential nomination, but his campaign never gained traction and he was essentially frozen out of major GOP debates and events. Since then, he has announced that he will instead seek a third-party nomination for the ballot.

"What I tried to do in this campaign — I've been unsuccessful so far — [well], I've had modest success — is appeal to the outsiders, those who have an interest in the future of America, yet are not the inside special interests," Roemer said.

Roemer admitted his third-party bid amounted to a Hail Mary pass in an interview with the New Orleans Times-Picayune late last month.

"We're going to run a different type of campaign," said Roemer. "We're about to throw deep. We only have a little bitty football, but we're going to throw deep."