Christie is up for reelection next year and has already received his first Democratic challenger, with speculation bubbling that Democratic darling Newark Mayor Cory Booker could also decide to run.
And though Cuccinelli has not yet been awarded the GOP nomination, he's the heavy favorite, with some Virginia Republicans expressing private concerns that he'll be too conservative to win in a state that has tilted decidedly purple in recent years.
Priebus also said in terms of the presidential nominating process, the RNC would like to take greater control over the debate planning process, instituting a requirement that all contenders participate in a schedule of debates preset by the committee, or else face delegation penalties.
His comments come after a nominating cycle that went on for months, with more than 25 primary debates, some of which didn't include all the candidates. Critics complained that the drawn-out process ultimately hurt the GOP's eventual nominee, Mitt Romney.
"If you have 10 presidential candidates, and seven out of 10 or eight out of 10 will take whatever two-hour slot that is open to them, then you end up with a debate any time some cable network decides to hold one. You can’t control that situation. Our endeavor is to come up with some idea that helps us control that situation," he said.
That will be addressed in the review process, Priebus explained, along with half a dozen other issues Republicans said they'd like to improve upon in the upcoming presidential election. He added that he's confident that, with four years of review and revision ahead, the GOP will regain its electoral footing.
"I think in the year and a half that we had, I think we did a great job. Unfortunately, I think the other side did a great job for four years. I think that’s really what we’re coming down to," he said.