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U.N. Ambassador Susan Rice’s potential bid to become the next secretary of state appeared further in jeopardy Wednesday, with one key Republican practically warning President Obama not to send her nomination to the Senate.

“I would just ask the president to step back away from all the buzz around this, take a deep breath and decide who’s the best secretary of state for this country,” Tennessee Sen. Bob Corker said after a 90-minute meeting with Rice, who is under fire for her initial public explanation of the deadly consulate attacks in Libya.

Rice’s separate talks with Corker and Maine Sen. Susan Collins, another key Republican, marked her second day of Capitol Hill meetings in her effort to explain events surrounding the attacks Sept. 11 on the U.S. Consulate in Benghazi, Libya.

She said five days after the attacks, on several Sunday talk shows, that the strikes appeared to be “spontaneous” acts of violence that evolved from protests over an anti-Islamic film.

Rice acknowledged to the senators that her initial account was wrong, but she insisted she had not been trying to mislead the American people.

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"The talking points provided by the intelligence community, and the initial assessment upon which they were based, were incorrect in a key respect: There was no protest or demonstration in Benghazi," Rice said in a written statement after the meeting.

Rice, who was accompanied to Capitol Hill by acting CIA Director Michael Morell, met Tuesday with the three Republican senators most vocal in demanding a detailed explanation: Lindsey Graham of South Carolina, Kelly Ayotte of New Hampshire and John McCain of Arizona, the ranking Republican on the Senate Armed Services Committee. The meetings were followed by one Tuesday afternoon with Sen. Joe Lieberman, an independent from Connecticut.

Should Rice be nominated by Obama, she would need to win support of several Republicans in the Democrat-controlled Senate to receive enough votes to be approved.

Her visits to Capitol Hill were unusual despite the outcry over her comments because only nominees typically meet privately with lawmakers, which appears to show Obama’s support for her efforts.

The president surrounded Wednesday by his Cabinet members -- including Rice -- said he could not be prouder of the job she has done. He also called Rice "extraordinary."

Hillary Clinton is soon expected to step down as secretary of state.

Jim Carafano, a foreign policy expert at the conservative think tank Heritage Foundation, said both sides had an interest in meeting.

The White House needs to get the story out of the news to continue with other appointments to national security-related posts. And Republicans were trying to “look for an off ramp” because after weeks of pressing Rice they were beginning to look like villains, he suggested.

“Each was looking for an exit strategy, but I was just stunned by the outcome of the meetings,” Carafano said. “This has to go down as one of the most complete and utter failures in Washington history.”

To be sure, the Republicans senators who met with Rice said they would approach her nomination with an open mind, but they expressed little optimism that Rice would get the post.

“I am more disturbed now than before,” Graham said after meeting with Rice.

Carafano also said “only those who really know” can say why Obama hasn’t pushed instead for Massachusetts Democratic Sen. John Kerry, chairman of the chamber’s Foreign Relations Committee, to fill Clinton's shoes.

“John Kerry would be an excellent appointment and easily be confirmed by his colleagues," Collins said.

The Associated Press contributed to this report.