Cain on "mission," and talks Defense sec'y. spot

One name that's missing from the Iowa caucuses is Herman Cain.

He suspended his presidential campaign last month in the face of escalating accusations of sexual misconduct.

He promised not to go away -- and he hasn't.

Video: Memorable moments from the campaign trail

Pictures: On the trail in Iowa

Cain said on "The Early Show" that, though he isn't in the running for president anymore, he hasn't "abandoned the mission" which, he said, "is to help get Barack Obama out of the White House."

He says he's starting a "movement," to "keep attention on solutions." He said, "One of the things that has frustrated me and many of the American people has been all of the negative attacks that have taken place during this campaign. ... Secondly, it takes attention away from how you're going to fix stuff. This is what the American people want. When I was in the campaign and I was at the top of the polls, it was the fact that people were connecting with solutions. And so what I plan to do is continue to promote solutions to problems, because not enough attention is being paid to them."

When asked if he endorsed any of the remaining candidates, Cain responded, "I'm not going to endorse anyone right now, but, when I do make an endorsement, it will be unconventional. Remember, I'm the unconventional candidate with unconventional ideas."

Cain has recently said if a Republican were to defeat Mr. Obama, he would be interested in the Secretary of Defense position in a new administration, CBS News' Chief White House correspondent Norah O'Donnell pointed out.

"That is a big job to serve as Secretary of Defense," she remarked to Cain. "I just want to ask you a couple questions. You had some mistakes on the campaign trail. You were confused about the Taliban. You said you thought the Taliban might take control in Libya. You know that the Taliban are not in Libya, correct?"

"Correct," Cain said, adding, "Norah, look, it's a learning process, and there are a lot of things that I have learned as a result of having been in the campaign, as well as after the campaign. Now, the reason that I indicated that I would consider being Secretary of Defense, I don't think that my qualifications of being the Secretary of Defense should be based on something I said months ago in error. No, it should be based upon leadership. National security is one of our biggest challenges that we have in this country, and I believe that, as a leader in that position, if we have the right president, I would be able to bring a lot to the party in terms of helping to prioritize those things that need to be prioritized."

CBS News chief Washington correspondent Bob Schieffer said, "Mr. Cain, wouldn't you have to start out being fairly familiar with the basic national security issues are? I mean, you throughout the campaign seemed unaware of a lot of the things that the Secretary of Defense would have to deal with. I mean, good intentions are one thing and bringing fresh insight. But do you really, sincerely, feel that you have the background and really the knowledge that you could handle a cabinet-level position like that?"

"Bob, allow me to remind you of something that didn't get picked up when I was beat up about what I didn't know. I served on the Citizens Advisory Board of the Strategic Air Command in Omaha, Nebraska, for several years when I was there. I was exposed to some of those issues at that particular time. I started my career as a ballistics analyst with the ... Navy. I've actually been on a Navy ship. So, I have been around some of these issues. So, it's not that I'm totally -- "

Schieffer interjected, "Sir, if I may interrupt. I have been on a Navy ship, too, but I don't think that qualifies me to be Secretary of Defense."

"Bob, I didn't say that qualified me to be Secretary of Defense," Cain said. "There you go...when I'm trying to make a point. That's not the point, Bob. I didn't say being on a ship one time qualifies me for being Secretary of Defense. My point is quite simply this: We need strong leadership in that position. And it was a hypothetical question and I gave a response based upon the question that was asked."

O'Donnell then posed this question: "How many people serve in the armed services?"

"We have about three million people who serve in the armed services," Cain said. "Was that a 'gotcha' question, Norah?"

"Yeah, we have 1.6 (million) who are active duty and two million total, if you include reservists who are part of our armed services." O'Donnell said.

Schieffer also asked Cain for his response to an accusation presidential hopeful Newt Gingrich leveled at Mitt Romney -- that he is a liar.

Gingrich: Mitt Romney is a liar

Schieffer said, "We had kind of an extraordinary little interview with candidate Newt Gingrich just a while ago. And, basically, talking about the attacks that Mitt Romney has leveled on him, he said, flatly, yes. That Mitt Romney is simply a liar. And I went on to ask him, 'Can you endorse him if he decides if he gets the nomination?' and he said, 'Well, yes, he could. Because, even though he's a liar, he's better than Barack Obama.' What did you come away from the campaign thinking about Mitt Romney? Do you agree with Newt Gingrich that he is in Gingrich's word a 'liar'?"

Cain replied, "Bob, as you know, political speak and you can choose the words. In political speak, it could have been stated as, he was not totally honest. And Newt has called him out on this.

"But you have to raise the same question with every candidate, including the current president. Can you honestly say that the current president has been 100 percent truthful about everything that he said? I think if we were to do the analysis, you would have to come away and say, 'Well, some of them may not have been as truthful as they would have been.' I think it is a choice of words, not as strongly as, he would support a liar. That's my opinion."

O'Donnell remarked, "It is interesting that you bring up the question of truthfulness, because what drove you from the campaign were questions about your own truthfulness in terms of your relationship with women. I do want to ask you ... how is your wife?"

"My wife is doing marvelous, thank you," Cain said. "We were blessed to have our fourth grandchild on New Year's Day. So, 2012 has gotten off to a great start for my wife and I. She is doing fine because since I got out of the race, we don't have to constantly hear the spinning and the re-spinning of those false accusations.

"And so, you are absolutely right. From that standpoint, she is great. And she is very supportive of this national movement that I'm going to be launching later this week in order to keep attention on what's really important in this," Cain said. "The whole Iowa caucus, with all due respect, it should narrow the field. The same thing should happen with New Hampshire. So, as the field narrows, I think and I hope that people will get back to paying more attention to how are these candidates going to fix problems? That's what the American people are looking for."