United Nations Ambassador Susan Rice, who may be tapped as President Obama's next secretary of state, met privately Tuesday with three Republican Senate critics to defend her role in the aftermath of the deadly Sept. 11 attack on the U.S. consulate in Libya. But lawmakers said Rice did nothing to allay their concerns.

Sens. Lindsey Graham of South Carolina, Kelly Ayotte of New Hampshire and John McCain of Arizona told reporters after the hour-plus meeting that they were "significantly troubled" by Rice's answers to their questions about the attack in Benghazi.

"All I can say is that the concerns I have are greater today than they were before, and we're not even close to getting the basic answers," Graham said.

Lawmakers questioned why Rice was still insisting days after the attack that the armed assault was a spontaneous, violent reaction to an anti-Muslim video, even though the CIA had determined early on that it was a planned attack by terrorists affiliated with al Qaeda.

"Clearly, the impression that was given, the information given to the American people was wrong," Ayotte said. "In fact, Ambassador Rice said today, absolutely it was wrong."

Rice said Tuesday that she was relying on erroneous information provided by U.S. intelligence sources at the time and insisted the administration wasn't purposely misleading the public prior to the election.

"We certainly wish that we had had perfect information just days after the terrorist attack," Rice said in a statement. "As is often the case, the intelligence assessment has evolved."

(Read the full statement at the bottom of this story)

Obama has yet to announce who he will select to succeed Secretary of State Hillary Clinton, who is said to be eager to step down at the end of the year. Rice is widely seen as Obama's top choice, followed by Sen. John Kerry, D-Mass.

The White House is concerned that elevating Kerry to secretary of state could cost Democrats Senate seat in Massachusetts. But nominating Rice also carries risks, including days of hearings at the start of the president's new second term in which Benghazi would be front and center.

A CNN poll released Tuesday showed 54 percent of those surveyed were "dissatisfied" with the Obama administration's response to the attacks, which killed Ambassador Chris Stevens and three others. The survey showed 40 percent believed the administration intentionally misled the nation about what happened.

The three senators said after Tuesday's meeting that they want more answers about Benghazi before they would even consider Rice as Clinton's replacement. They have called for a select committee to investigate the attack, but Senate Majority Leader Harry Reid, D-Nev., has refused to create one.