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“He’s on the horns of a dilemma here,” former Sen. Evan Bayh of Indiana said on “Fox News Sunday.” “If he doesn’t nominate her, he looks weak. If he does nominate her, he has a fight on his hands, and potentially, [a] somewhat polarizing secretary of state figure.”

Mr. Bayh said his best guess is that the president will “choose to go forward and try and persuade the critics” that their reservations are baseless, “that there is really no there, there.”

Nomination doubts

Last week in a statement, Mrs. Rice said she had relied “solely and completely” on talking points prepared by the U.S. intelligence community.

But her belated acknowledgment that the assessment on which they were based was wrong has done nothing to mollify her critics.

Sen. Kelly Ayotte, a member of the Senate Armed Services Committee, said Mrs. Rice had read classified intelligence briefings noting that al Qaeda supporters were involved in the attack but did not mention that in her television interviews in the days afterward.

The New Hampshire Republican also said that Mrs. Rice relayed information on television that was not in the briefings, including inaccurate claims about the consulate’s security and al Qaeda’s strength in the region.

The ambassador “went beyond the talking points,” by saying al Qaeda had been “decimated” and calling the security at the mission, at different points in several interviews “strong substantial and significant,” Mrs. Ayotte said on CNN’s “State of the Union.”

Mrs. Rice’s explanations are “frankly, not supported by the record,” she said.

Mr. Graham said Mrs. Rice “had told a political story designed to help the president three weeks before an election,” and that he is hard-pressed to see how he might be able to support her nomination.

“I find her lacking when it comes to being the best choice for secretary of state. But this is up to the president,” he said.

But the man in line to be the ranking Republican on the Senate committee that would vet her nomination said he does not think Mrs. Rice will be the nominee.

“I don’t think she’s going to be nominated,” said Sen. Bob Corker, Tennessee Republican and a senior member of the Senate Foreign Relations Committee. “I’ve told people certainly I’ll give her a fair hearing. … The underlying issue [with her confirmation] is people have seen her far more as a political person and not as a principal, and I think that’s what the White House is witnessing now.”