From left, Chris Christie, Grover Norquist and Jeb Bush are pictured.

Editor’s Note: Party People is a new podcast from CNN where a pair of conservative CNN contributors talk to influential voices about the future of conservatism and the Republican party.

Story highlights

Grover Norquist says he wants governors to have a bigger say in the future of the Republican party

He highlighted successes from Scott Walker, Jeb Bush and Chris Christie in an interview

CNN  — 

Many Republicans aren’t happy with how the primary process shook out in 2016; Donald Trump is their presidential candidate and his campaign has hit some speed bumps.

But Grover Norquist has one idea he thinks can lead to different results: Have primary debates moderated by governors and other Republican leaders.

“My fix, which I still like: You start with four debates,” the Americans for Tax Reform president told CNN’s “Party People” podcast hosts Kevin Madden and Mary Katherine Ham in a recent conversation. “The first one (is) all the candidates in front of the governors who are not running for president, and they have to discuss politics in front of Republican governors. I don’t think Trump could have called somebody long face or small hands or whatever it is and gotten past the governors going, ‘Excuse me, I was asking about Medicare and Medicaid.’”

Grover Norquist: Donald Trump still hasn’t signed tax pledge

Norquist’s proposal for the next three primary debates would have a similar format, one being hosted by members of Congress, another being hosted by Republican party officials and the last one being held by Republican appointed ambassadors to address foreign policy issues.

Norquist took issue with the current system because, he said, debate moderators throughout the primaries – TV journalists, for the most part – set the agenda.

“Because the moderators thought that gay marriage was a fascinating topic, they asked about that all day,” Norquist said, adding later, “We allowed the moderators to decide what the Republican party was perceived as caring about.”

Despite the drama surrounding the top of the ticket, Norquist had high praise for state level Republicans as a sign of the party’s future, saying, “The modern Republican party is extremely healthy.”

In particular, Norquist praised actions by former Florida Gov. Jeb Bush, Wisconsin Gov. Scott Walker and New Jersey Gov. Chris Christie, as Republican leaders who made significant strides shaping the party for the better.

“I almost want to pass a Constitutional amendment saying only governors can run for president so that you can prove you can do it,” he said. That’s not an amendment that would be very likely to get through the US Senate, where many presidential candidates spend part of their career.

To hear how Norquist feels about his no-tax-increase pledge and how he starting going to the Burning Man festival, listen to CNN’s “Party People,” a new podcast from CNN where a pair of conservative CNN contributors talk to influential voices about the future of conservative politics and the Republican party.

Get CNN’s “Party People” podcast at CNN, Stitcher, TuneInRadio or iTunes.