Some Republicans rankled at how those debates were handled, complaining especially loudly about CNN anchor John King's line of questioning during a South Carolina debate.
The move comes as the RNC is considering how to limit the number of debates heading into 2016, and threatening to ban CNN and NBC for hosting debates because of their networks' plan to run a miniseries focused on Hillary ClintonHillary Rodham ClintonFlight attendant union backs Clinton Gingrich: Ex-Miss Universe 'the new Benghazi lie' Tina Fey suggested Alec Baldwin for SNL's Trump MORE.
RNC Chairman Reince Priebus said having conservative radio hosts moderate a debate was a "good idea" last week, while RNC Communications Director Sean Spicer suggested having Levin as a moderator earlier this week.
Some potential candidates could balk at that decision, however. Levin has been highly critical of New Jersey Gov. Chris Christie (R), while Limbaugh spent months ripping a Senate immigration plan backed by Sen. Marco RubioMarco RubioOvernight Finance: Lawmakers float criminal charges for Wells Fargo chief | Scrutiny on Trump's Cuba dealings | Ryan warns of recession if no tax reform The Trail 2016: Just a little kick Opposition to Obama's radical disarmament agenda has proven effective MORE (R-Fla.). Both Christie and Rubio are considered possible 2016 candidates.