In emotional testimony last week before the Senate and House, Clinton said she took "responsibility" for the security failings.
"It is our responsibility to make sure they have the resources they need to do their jobs and to do everything we can to reduce the risks they face," Clinton told the Senate Foreign Relations Committee. "For me, this is not just a matter of policy — it’s personal."
Graham also reiterated his threat to block the nomination of former Sen. Chuck Hagel (R-Neb.) to lead the Defense Department unless the current secretary of Defense, Leon Panetta, agrees to testify on the Benghazi attack.
"The one thing I’m not going to do is vote on a new secretary of Defense until the old secretary of defense, Leon Panetta, who I like very much, testifies about what happened in Benghazi,” said Graham.
Graham did not rule out an eventual vote for Hagel, however, telling Fox News host Greta Van Susteren that "it will depend on what he says in the hearing Thursday."