Possible promotions for U.N. Ambassador Susan Rice and acting CIA Director Michael Morell remain in jeopardy after the two officials met Tuesday with three of their Republican critics regarding how the Obama administration responded to the attacks on a U.S. diplomatic outpost in Libya.

“Bottom line, I’m more disturbed now than I was before,” Sen. Lindsey Graham (R-S.C.), one of the critics, said after the meeting.

Rice and Morell are reportedly under consideration to serve as the next secretary of state and CIA director, respectively. They met Tuesday morning on Capitol Hill with Sens. John McCain (R-Ariz.), Graham, and Kelly Ayotte (R-N.H.), who have led a GOP charge against the administration since the Sept. 11 attack on a U.S. diplomatic outpost in Benghazi, Libya, that led to the deaths of four Americans, including Ambassador J. Christopher Stevens. Rice and Morell later met separately with Sen. Joseph I. Lieberman (I-Conn.), whose homeland security committee is also probing the attack.

The Republican senators have repeatedly said they are concerned with how Rice explained what caused the Benghazi attack during a series of Sept. 16 appearances on Sunday political talk shows. At the time, Rice said that a spontaneous demonstration led to the violence, a claim later debunked by intelligence officials and reports from the ground.

The White House and senior intelligence officials have said that Rice’s statement followed talking points they had approved, including vague wording designed to conceal intelligence information. Rice said that “extremist” elements had participated in the attack, and that the conclusions were preliminary pending FBI investigation.

Rice and Morell slipped into the Capitol on Tuesday unseen by reporters. After her meeting with the Republican senators, Rice said there was no intent on her part or on the part of the administration to mislead American citizens.

“In the course of the meeting, we explained that 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 statement. “While, we certainly wish that we had had perfect information just days after the terrorist attack, as is often the case, the intelligence assessment has evolved. We stressed that neither I nor anyone else in the Administration intended to mislead the American people at any stage in this process, and the Administration updated Congress and the American people as our assessments evolved.”

White House press secretary Jay Carney later rejected the Republican senators’ charge that Rice and Morell left questions unanswered.

“I would simply say that there are no unanswered questions about Ambassador Rice’s appearances,” on Sept. 16, Carney said. “The questions that remain to be answered, and that the president insists are answered, have to do with what happened in Benghazi, who was responsible for the deaths of four Americans including our ambassador and what steps we need to take to ensure that something like that does not happen again?”

The discussions with McCain, Graham and Ayotte were arranged “to go over exactly the very questions that those senators had,” Carney said, including the origin of the information Rice conveyed on television.

Carney called the focus on Rice’s television appearances “misplaced.”

But McCain told reporters that he and his colleagues remain “significantly troubled by many of the answers that we got and some that we didn’t get concerning evidence that was overwhelming leading up to the attack on our consulate that we tried to get.”

Lieberman sounded a more supportive tone after his meeting with Rice, saying she “told the truth to the best of her knowledge” on Sept. 16.

“I asked if she was briefed by the White House, the campaign, or the political operation, and she said she had seen no message points from the White House,” Lieberman said. “Nothing she said [on the Sunday shows] disqualifies her for any other office.”

As criticism of Rice’s statement intensified, Obama has attempted to buttress her from the attacks, saying he is ultimately responsible for what occurred in Libya. With some congressional Democrats charging that Republicans were targeting Rice because of her race and gender, McCain appeared to soften his criticism during his own Sunday talk show appearance over the weekend by saying he was willing to meet with her so she could explain herself.

But the rhetoric picked up again Tuesday as Graham said the group would place holds on Rice’s nomination, if she is nominated to lead the State Department succeeding Hillary Rodham Clinton, and on Morell’s, if he is tapped to succeed former CIA director David Petraeus.

“Before anyone can make an intelligent decision about promoting someone involved in Benghazi, we need to do a lot more. … We’re not even close to getting the basic answers,” Graham said.

Rice and Morell are also scheduled to meet with Wednesday with Susan Collins (R-Maine), who is joining Lieberman in the homeland security panel’s investigation.

Other Republican senators expressed tepid support for Rice on Tuesday, saying they will reserve judgment on whether they would vote to confirm her as secretary of state.

“She always reminds me of someone who’s had every drop of Kool-Aid, always espousing 1000 percent of whatever point of view the administration is putting forward,” said Sen. Bob Corker (R-Tenn.), a senior member of the Senate Foreign Relations Committee. But Corker said his meetings with Rice have always been “transparent and direct.”

Republican criticism appears to be catching on with Americans, according to a new poll.

A CNN/Opinion Research poll released Tuesday found that 54 percent of Americans disapprove of the administration’s handling of the Benghazi attack and 40 percent believe that initial statements about the incident were deliberately intended to mislead Americans.

A majority now also disapprove of the administration’s handling of the attacks, according to the poll. That’s up from roughly 40 percent of Americans who generally disapproved of the administration’s handling of the situation in Libya in a previous CNN poll.

This post has been updated since it was first published.

Staff writers Karen DeYoung, Anne Gearan and Aaron Blake contributed to this report.

Follow Ed O’Keefe on Twitter: @edatpost