Within minutes of President Obama’s warning not to interfere with his nominations, Republican Sen. Lindsey Graham made clear he wouldn’t back down from mounting a challenge if Susan Rice is nominated for secretary of state.

“Mr. President, don’t think for one minute I don’t hold you ultimately responsible for Benghazi,” the South Carolina Republican said in a statement. “I think you failed as commander in chief before, during and after the attack.

“Given what I know now, I have no intention of promoting anyone who is up to their eyeballs in the Benghazi debacle,” he said.

At issue are Rice’s Sunday talk show statements five days after the attack on the U.S. diplomatic mission in Benghazi that killed Ambassador Chris Stevens and three other Americans. She attributed the incident to the outrage in the Arab world over an anti-Muslim video, not terrorism.

Graham, Sen. John McCain, R-Ariz., and Sen. Kelly Ayotte, R-N.H., are pressing for a special, Watergate-style select Senate committee to investigate the attack. They complained that separate inquiries by various Senate panels will fail to get to the truth and a comprehensive probe “up to and including the president of the United States” was warranted.

Sen. Olympia Snowe, R-Maine, meanwhile, said she had yet to make a decision about who is the best person to fill the secretary of state position. But Snowe called Rice’s televised statements immediately after the Sept. 11 attacks in Benghazi “so detached from the reality and what ultimately occurred.”

“It does raise concerns,” Snowe said. “That would be an issue that she would have to address if she were the nominee.”