WASHINGTON -- Republican opposition to the potential nomination of United Nations Ambassador Susan Rice as secretary of state appeared to harden Tuesday after she met behind closed doors with three key Republican senators.

What was supposed to be a session to clear the air and lower tensions seemed to have had the opposite effect as Sens. Kelly Ayotte of New Hampshire, Lindsey Graham of South Carolina and John McCain of Arizona said they’d left their morning meeting with Rice and acting CIA Director Michael Morell with more questions than answers about comments she’d made in the initial aftermath of the deadly attack Sept. 11 on U.S. diplomatic facilities in Benghazi, Libya.

“We are significantly troubled by many of the answers that we got and some that we didn’t get, considering evidence that was overwhelming leading up to the attack on our consulate, the tragic deaths of four brave Americans and whether Ambassador Rice was prepared or informed sufficiently in order to give the American people a correct depiction of the events that took place,” McCain said.

At the White House, Press Secretary Jay Carney said Rice’s critics had developed “an obsession” over the talking points she used on five Sunday morning talks shows five days after the attack.

Carney said that some had "focused on this for what appear to be political reasons when the issue that matters is what happened to those four Americans and who was responsible and what can we do to make sure it doesn’t happen again.”

He added that "the focus on a Sunday show appearance is entirely misplaced, and it represents less interest, I think, in what happened in Benghazi than in political dynamics in Washington."

Rice has been mentioned as a possible successor to Secretary of State Hillary Clinton, who’s indicated that she won’t serve in President Barack Obama’s second term. White House officials won’t comment on whether the president intends to nominate Rice, though he’s offered a full-throated defense of his embattled U.N. ambassador.

Rice’s critics in the Senate have responded that they’d block her nomination until they got more answers on Benghazi.

“We’re not going to consider this nomination until we get basic answers to our concerns,” Graham said.

Sen. Carl Levin, D-Mich., the chairman of the Senate Armed Services Committee, said he doubted that the Benghazi incident would derail a Rice nomination.

“Most Republicans are fair,” Levin said. “And when they see that she was simply using something that was produced by the consensus of the intelligence community they’re going to say, ‘Why would we hold against her if there were any statements there that were changed subsequently? Why would we hold it against a consumer of that product?’ . . . It’s so fundamentally wrong to hold that against her.”

Republicans charge that Rice on the talk shows described the attack as stemming from a spontaneous protest against an anti-Islam video and not as a terrorist operation in a deliberate bid to protect Obama’s record on terrorism in the closing weeks of his re-election campaign.

U.S. Ambassador Chris Stevens and Information Management officer Sean Smith were killed when the consulate came under attack. Several hours later, two other Americans, Glen Doherty and Tyrone Woods, died at a CIA compound a mile away where surviving Americans from the consulate fled. Libyan officials investigating the attack told McClatchy they think that the attackers followed those who were fleeing. Doherty and Woods died from mortar rounds shot into the CIA compound.