Sen. John McCainJohn Sidney McCainHeitkamp becomes first Dem to back Pompeo for secretary of State Senate committee sets Monday vote even as Pompeo appears to lack support Trump checkmates Democrats in sending Pompeo to North Korea MORE (R-Ariz.) late Monday said White House press secretary Jay Carney has "destroyed his reputation" because of a statement he made about Benghazi last week.

"He has destroyed his own reputation by that statement that clearly was the talking points, which had nothing to do but Benghazi, saying it had nothing to do with Benghazi. That, to me, is an all-time low for a presidential spokesperson," McCain said on Fox News’s "On the Record."

McCain said he’s known Carney for years, and had viewed him as a "pretty straightforward journalist."

Last Wednesday, Carney said an email released by the White House about Benghazi talking points after the attack referred to the Muslim world in general, but it wasn't specifically about Benghazi. 

"The email and the talking points were not about Benghazi," Carney said at a press briefing. "They were about the general situation in the Muslim world."

"They are scared to death," McCain said, referring to White House officials.

McCain said he would "love" to see Senate Majority Leader Harry Reid (D-Nev.) form a bicameral select committee to investigate Benghazi, but added "Obviously, that won't happen." Speaker John Boehner (R-Ohio) on Friday announced a proposal to form one in the House.

If Democrats refuse to participate in the committee, McCain said "they are the ones that will have egg on their faces."

McCain, Sens. Lindsey Graham (R-S.C.) and Kelly Ayotte (R-N.H.) sent a letter to President Obama on Friday asking where he was the night of the attack that September.

"All we know is that he was briefed by [Leon] Panetta and Dempsey and they left, and there was no further communication," McCain said Monday. 

At the time, Panetta served as secretary of Defense and Martin Dempsey was and still is chairman of the Joint Chiefs of Staff.