Though Petraeus is not expected to testify at the committee’s closed-door hearing next week, Chambliss said on ABC’s This Week that Petraeus’s testimony will likely happen later. “He’s trying to put his life back together right now and that’s what he needs to focus on,” Chambliss said.

Speaking on Fox News Sunday, Senator Dianne Feinstein, the California Democrat who chairs the committee, also said Petraeus would likely testify eventually.

Speaking on CBS’s Face the Nation, Sen. Lindsey Graham, R-S.C., who has been among Republican senators loudly urging hearings on Benghazi, called it “absolutely essential.”