GOP senators not satisfied with Rice explanation of Benghazi aftermath ET -- Republican senators emerged from their meeting Tuesday with United Nations envoy Susan Rice saying they were more disturbed than before the meeting about the misleading explanation she gave after the Sept. 11 attack on the U.S. consulate in Benghazi, Libya, when Rice said in TV interviews that the violence was due to an anti-Islamic video that was circulated on YouTube. Senators John McCain, Lindsey Graham, and Kelly Ayotte stated that, after meeting with Amb. Susan Rice, they are more "troubled" and still have many questions regarding the administration's handling of Benghazi. Rice, a potential nominee to replace Secretary of State Hillary Clinton, met with Republican Senators John McCain, Lindsey Graham and Kelly Ayotte. The three senators have been among the harshest critics of the administration's handling of Benghazi and all spoke with reporters following Tuesday's meeting. It is clear that the information she gave the American people was incorrect when she said that it was a spontaneous demonstration triggered by a hateful video. It was not, and there was compelling evidence at the time that that was certainly not the case," said McCain. In the Sept. 11 assault on the consulate, Ambassador Chris Stevens and three other Americans, Glen Doherty, Tyrone Woods and Sean Smith, were killed. Graham said, "Bottom line: I'm more disturbed now than I was before that the 16th (of) September explanation of how four Americans died in Benghazi, Libya by Ambassador Rice I think does not do justice to the reality at the time and in hindsight clearly was completely wrong." Graham suggested that Rice should have simply not made any statement on the Sept. 16 Sunday TV talk shows. "If you don't know what happened, just say you don't know what happened," Graham said. If you can do nothing but give bad information, isn't it better to give no information at all? United States Ambassador Susan Rice speaks during a meeting on Syria in the United Nations Security Council on Thursday, Aug. 30, 2012. He added, "Before anybody can make an intelligent decision about promoting someone involved in Benghazi, we need to do a lot more (investigating). To this date we don't have the FBI interviews of the survivor one or two days after the attack.  He invoked the example of President Bush's nominee to be UN ambassador, John Bolton, who was blocked by Senate Democrats and a few Republicans in 2005 and 2006, implying that if Rice were nominated to the secretary of state Republicans would likewise block her confirmation. Ayotte, too, said she was "more troubled" after meeting with Rice and Acting CIA Director Mike Morrell than she was before the meeting. She questioned why Rice would have relied on unclassified CIA talking points in her TV interviews on Sept. "When you're ambassador to the United Nations you go well beyond unclassified talking points in your daily preparation responsibilities for that job and that's troubling to me as well," Ayotte said. In a statement released Tuesday afternoon, Rice said that she and Morrell had explained to the senators in the meeting Tuesday 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. 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. Last week Graham sent Obama a letter saying, "We have now learned that the talking points provided to Ambassador Susan Rice on or around September 15 describing the assault on our consulate in Benghazi were disconnected from the actual intelligence. According to numerous sources, including CIA Director David Petraeus and the CIA station chief on the ground in Libya, the perpetrators of the attack were identified to be al Qaeda-linked militia almost immediately. Graham told Obama that by the time Rice spoke on five Sunday TV talk shows on Sept. 16, "the classified intelligence clearly refuted the scenario she described." He asked Obama to explain why Rice was chosen to explain the attack to the American people. Why wasn't someone with firsthand knowledge of the attack on our Consulate, or firsthand knowledge of the administration's response during the critical hours our consulate was under attack, selected for this opportunity? Sen. Bob Corker, R-Tenn., who is in line to become the senior Republican on the Senate Foreign Relations Committee in the new Congress that convenes in January, said Tuesday he sees Rice as a party loyalist. "When I hear Susan (Rice) talk, she sounds to me like she'd be a great head of the Democratic National Committee," Corker told reporters at the Capitol. There's nobody who's more staff supportive of everything the administration does. That concerns me in a Secretary of State. You want a Secretary of State who obviously works with the administration but also shows the ability to be independent, and I'm not sure I see that second part. The Senate has not voted to reject a nominee for a Cabinet position since 1989 when it voted down President George H.W. Bush's nomination of John Tower to be secretary of Defense. Unlike that case, the Senate is now controlled by the president's own party. NBC News's Frank Thorp contributed to this report.