WASHINGTON -- A visibly annoyed President Barack Obama and tough-talking Senate Republicans clashed sharply Wednesday over Susan Rice’s qualifications to become secretary of state, a strong reminder that all the post-election talk about bipartisanship has its limits.

The fight started with trial balloons in the news media this week signaling that Obama plans to nominate Rice as secretary of state when Hillary Clinton steps down

Two Republican senators responded Wednesday. Sen. John McCain of Arizona called Rice “not qualified,” and Sen. Lindsey Graham of South Carolina said flatly, “I don’t trust her,” because of her statements about the Sept. 11 attack in Benghazi, Libya, that killed four Americans.

Obama, in an unusual show of emotion Wednesday, defended Rice, the United Nations ambassador who’s been a mainstay of his foreign policy team since his 2008 campaign.

“If Senator McCain and Senator Graham want to go after somebody, they should go after me,” he said at a White House news conference. “To besmirch her reputation is outrageous.”

Rice has been under fire ever since she was dispatched by the Obama administration to tell Sunday talk shows five days after the Libya incident that it resulted from a spontaneous demonstration, a narrative that turned out to be false.

In defending Rice Wednesday, Obama may have inadvertently suggested she lacked the stature of a secretary of state, arguing that she was only a spokesman on the Libya story, reciting talking points given her by intelligence agencies.

“For them to go after the U.N. ambassador who had nothing to do with Benghazi?” Obama asked. “And was simply making a presentation based on intelligence that she had received?”

Republicans weren’t buying that.

“This is about the role she played around four dead Americans when it seems to be that the story coming out of the administration – and she’s the point person – is so disconnected to reality, I don’t trust her,” said Graham. “The reason I don’t trust her is because I think she knew better, and if she didn’t know better, she shouldn’t be the voice of America.”

Unfair, protested Obama.

“But when they go after the U.N. ambassador, apparently because they think she’s an easy target, then they’ve got a problem with me,” Obama said. “If I think that she would be the best person to serve America in that capacity at the State Department, then I will nominate her.”

After the press conference, Graham, often considered a Republican who works well with Democrats, wouldn’t let up.

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

The fight comes at a post-election time when the two parties have signaled they want to work together. The Rice flap throws a grenade into the works.

Having Rice in the mix “doesn’t help,” said Sen. Orrin Hatch of Utah, a Republican with a history of finding bipartisan consensus.

Presidents and senators try to avoid nomination fights, partly because opponents traditionally believe a president is entitled to his team, and partly because they don’t want to start off a year on an ugly note.