Graham, a member of the Senate Foreign Relations Committee, said on CBS's "Face the Nation" that he would seek to block votes on Chuck Hagel as defense secretary and John Brennan as CIA director until he gets a better explanation of what the president was doing during the attack in September on the U.S. consulate in Benghazi, which killed four Americans, including Ambassador Christopher Stevens.
"This is a complete system failure, and I'm going to get to the bottom of it," he said.
Graham said he would put a hold on the two confirmation votes. Under Senate rules, a hold can be a tough procedural obstacle. Sixty votes are needed to end a hold and bring a motion to the Senate floor.
Republican critics, including Graham, have been hammering at the administration's response since shortly after the raid in September, criticizing early statements that linked the attack to demonstrations to a video that was critical of Islam. On Sunday, Graham raised asked whether the president intervened to try to speed more help to the besieged compound.
"I don't know what the president did that evening. I don't know if he ever called anyone," Graham said.
Democratic Sen. Jack Reed of Rhode Island, also appearing on the program, said that Graham's threat was "unprecedented and unwarranted."
He said Graham had the right to ask "legitimate questions," but not to try to block the nominations from an up-or-down vote. He called it "an overreaction that is not going to serve the best interest going forward of the national security of the United States."
It's not clear how much support Graham's move would have among fellow Republicans. Sen. John McCain said Sunday that he was leaning toward voting against Hagel, a former Republican senator from Nebraska, saying he had "grave concerns" about his suitability.
But McCain also said he thought it would be wrong to invoke a filibuster to thwart a president's Cabinet choices, although he didn't address the use of holds.
"We've never filibustered a presidential cabinet appointee, and I don't think we should start here," he said on "Fox News Sunday." "Elections have consequences, unfortunately."
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