"I have serious concerns about where we are right now and trusting what she has to say, but I'm willing to listen to what she has to say," Ayotte added.

Republican Sen. Rand Paul of Kentucky told CNN's "Erin Burnett OutFront" that someone should lose their jobs over Benghazi but Rice should not be the issue. He said security questions are paramount.

"I think really the more important question isn't really about whether it was caused by terrorism or whether it was caused by a movie," he said. "Obviously it was terrorism, but I think the more important question is why were there no Marines guarding our ambassador. Who made the decision -- not an immediate... decision, but a month-long desk decision to send an ambassador into a war-torn country without any uniformed Marines."

Paul said he did not want to "pre-judge" any nomination for the secretary of state.