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Sometime before the attack, he said, officials considered moving the CIA operation (based in a nearby annex) on-site with the consulate, but rejected the mission compound as “too insecure.”

Mrs. Rice was not involved in any decisions about security at Benghazi, but she became the focus of attention after widespread reports that she soon will be nominated to succeed Mrs. Clinton, who has said she wants to step down as secretary of state.

Democrats the focus on Mrs. Rice is a waste of time until she is nominated for the post.

“What I find remarkable is, the president hasn’t even nominated anyone yet,” Mr. Warner said on the CNN program.

Sen. Dianne Feinstein, California Democrat and chairwoman of the Senate Select Committee on Intelligence, has said she is concerned about security at other U.S. diplomatic missions in volatile areas, such as Sanaa, Yemen; and Peshawar, Pakistan.

‘Not about Susan Rice

Last week, several Republican senators openly threatened to block Mrs. Rice’s confirmation if she is nominated. But in another interview Sunday, one of her fiercest Republican critics said the issue goes well beyond her role.

“It’s not just about Susan Rice. It’s about a system that failed. The military failed. The intelligence community failed, before and during [the attack]. This is about a system designed to protect us which completely broke down,” Sen. Lindsey Graham of South Carolina said on “Face the Nation.”

Mr. Graham, a member of the Senate Armed Services Committee, said he is troubled by the apparent inability of the U.S. military to get any help to the embattled State Department and CIA personnel as the two-stage attack unfolded over more than seven hours during the night of Sept. 11.

“Why for seven hours on Sept. 11 we could not reinforce the compound?” he said.

Defense Secretary Leon E. Panetta has said that — despite the presence of a U.S. surveillance drone flying over the scene and CIA security contractors on the ground — there was insufficient intelligence to send troops into harm’s way or authorize other military action, such as an airstrike, inside a country with which the United States is not at war.

Mr. Graham contrasted the minute-by-minute account of Mr. Obama’s role in the Navy SEAL raid that killed Osama bin Laden, which the White House made public, with its silence about the commander in chief’s actions on the night of the attack.

“We don’t know anything about what he did on Sept. 11,” Mr. Graham said of the president. “Did the president order the military and others to come to their aid? And if he did, when did he make that order? When was he first notified?”

Mr. Obama has strongly backed Mrs. Rice, calling her “exceptional.”

But the president’s public support of the embattled diplomat has led one Democrat to wonder whether the president has painted himself into a corner.

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