Image credit: Tom Williams/Getty Images

Updated at 4:38 p.m. ET

President Obama was visibly angry today after Sens. John McCain and Lindsey Graham pledged to block Susan Rice, a potential Secretary of State, over her role in explaining the aftermath of the Sept. 11th attack on the U.S. consulate in Benghazi.

"They should go after me," he said.

Obama has not yet nominated Rice, but she is considered a potential frontrunner for the post. McCain, R-Ariz., and Graham, R-S.C., today said they would seek to block a potential nomination because, as Graham put it, she is "up to her eyeballs in the Benghazi debacle."

The pledge to stand in Rice's way if he eventually nominates her drew an uncharacteristically sharp rebuke from President Obama at a rare Washington, D.C. press conference.

"If Senator McCain and Senator Graham and others want to go after somebody, they should go after me," said Obama. "And I'm happy to have that discussion with them. But for them to go after the U.N. ambassador, who had nothing to do with Benghazi and was simply making a presentation based on intelligence that she had received and to besmirch her reputation is outrageous."

Read more about Obama's first post-election press conference .

Graham shot back with a paper statement responding to Obama.

"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.

"If the president thinks that we are picking on people, he really does not have any idea of how serious this issue is," said McCain on the Senate floor.

"This president and this administration has either been guilty of colossal incompetence or engaged in a cover-up, neither of which are acceptable to the American people," McCain said.

Graham and McCain also want a special blue ribbon committee like those that investigated Watergate or the Iran Contra affair appointed to look into the Obama administration's response to the September 11th terror attack against the U.S. consulate in Benghazi.

Rice is a longtime adviser to President Obama and is thought to be a frontrunner for the job if, as expected, Hillary Clinton leaves the Department of State. But she has become the target of Republican accusations about the administration's handling of the aftermath of the Sept. 11th attack on the U.S. Consulate in Benghazi that killed four Americans, including Amb. Chris Stevens, the top U.S. diplomat in Libya.

McCain said the Obama administration has no credibility in the investigation of what transpired before, during and after the attack in Benghazi. It was Rice who days after the attack appeared on ABC's This Week to argue the attack sprung from a spontaneous protest. It is now clear that it was a planned terrorist attack and parts of the U.S. national security apparatus knew it was terrorism before Rice appeared on This Week.

At a press conference Wednesday calling calling for the special select committee to investigate all aspects of what might have happened in the Benghazi attack, McCain said he would do everything in his power to block Rice if she is nominated, although he shied away from saying he would filibuster her nomination.

"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. "And 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."

Graham argued a special committee is needed to conduct a more thorough investigation of what happened in the aftermath of the Benghazi attack and tie together the work of three U.S. Senate committees currently conducting oversight.

The senators said they appreciate that Gen. David Petraeus will testify before the intelligence committee this week on his review of the Benghazi attack before he resigned as CIA Director amid a sex scandal. But they have questions for him too.

"We on the Armed Services Committee also have an interest in what General Petraeus has to say with this overlap of why we didn't have forces there who were ready to respond and questions like that, so there is significant overlap," said McCain. He argued that the Benghazi attack warrants a special committee because four Americans died.

"In Watergate, nobody died. In Iran-Contra, nobody died," he declared, pointing out that four Americans died in Benghazi. Democrats, particularly Senate Majority Leader Harry Reid oppose the committee, which makes it's formation unlikely.

McCain told ABC's Jonathan Karl at the Washington Ideas Forum earlier Wednesday that Petraeus did the right thing by resigning his post.

"It was his judgment, I respect his judgment," McCain told Jon Karl in response to the question of whether he believed Petraeus's decision to resign was the right thing to do. "I regret, as I think most everybody does, we regret the loss of his service to the nation."

But McCain does not see any wider conspiracy or national security threat from the growing sex scandal involving Petraeus, his biographer Paula Broadwell, who may have had classified documents on her computer, Gen. John Allen, the outgoing U.S. commander of forces in Afghanistan and a Tampa socialite.

"Well, I say with great respect, that's one of the dumbest questions I've ever heard, OK?" McCain said at the press conference on Capitol Hill.

See a timeline of the Petraeus investigation HERE.

The senior Republican Senators, who are known around Capitol Hill as something of a duo, dug in against the Obama administration on more than just Benghazi on Wednesday. They also argued to Karl at the Washington Ideas Forum that the president's decisive electoral victory Nov. 6th does not give him a mandate to raise taxes on the wealthy. The forum, which was held at the Newseum, is a two-day event sponsored by the Atlantic and the Aspen Institute and features a plethora of prominent thinkers and leaders in in the economic, political and foreign policy arenas, among other topics.

The two men did not mince words when talking about the challenges Republicans face with minority groups, which were highlighted last week in the election results.

"I think the Republican party has got to fully understand the results," McCain said. " We've got significant problems with the Latino vote and with young women. We need to get a lot of younger women and men involved in our party and give us their ideas and thoughts about their hopes and dreams and aspirations… One of challenges is immigration reform- we need to set about that as quickly as possible. But don't think that that's the panacea, we have a lot of work to do. We've got to base it on jobs, opportunity, family values, patriotism, small business, lower taxes, less government, and all the things that we stand for and believe in."

"It's one thing to get hit by a speeding bullet, it's another to get run over by a slow moving truck" Graham noted. "If you couldn't see this coming as a Republican you're just not looking out very well. We're going in the wrong direction… And you'll never convince me that it's not based on the fact that the immigration debate has alienated the Hispanic community when it comes to the Republican label."

Karl also questioned the prominent Senators about their outlook on the fiscal cliff negotiations, and whether they believed that the results of the general election gave Obama a mandate to raise taxes on the top income tax bracket. Neither McCain nor Graham agreed that the President had a mandate, but they both expressed a willingness to compromise in the ensuing discussions.

What's the "fiscal cliff" and how would it affect you? See the answer in our infographic HERE.

"I think that the agreement that we are searching for is a way to close loopholes without a specific agreement to raise tax rates," McCain said. "I think it's really going to come down to that - whether we actually raise rates or do away with many thousands of different subsidies… There are a whole lot of things we could do without specifically raising tax rates but it may come down to that."

"When you're 16 trillion in debt you need to rethink where you are and where you're going as a party," Graham said, referring to both Republicans and Democrats outlook. "How do you get out of debt? Both parties working together for a long period of time."

Sarah Parnass contributed to this report.