ABC News’ Michael Falcone reports:

CONCORD, N.H. – Although he has a tough primary battle ahead of him, rising-star presidential candidate Herman Cain today sought to portray himself as a strong general election candidate, one who could even draw black voters away from President Obama.

“Black people are going to vote for me not because I’m black,” Cain said, “but because of the strength of the ideas.”

Although he said race was a “non-issue” in the campaign, when asked whether he thought he could siphon off black voters from President Obama, he replied, “Oh, yes.”

The former Godfather’s Pizza CEO, who grew up in Georgia, also contrasted his background with Obama’s.

“His upbringing was very different from mine,” Cain said. “I grew up in the South during the 50s and the 60s. I was the son of a working dad who worked three jobs. We grew up in segregated areas and went to segregated schools. I’ve lived through the transitions that black people have gone through in this country, unlike President Obama. I still connect with all people in this country.”

He added, “My church is still in the hood. It’s the same church I grew up in.”

Cain, 65 and an ordained Baptist minister, attends the Antioch Baptist Church in Atlanta. He said the congregation is composed of people from all income levels. “I associate with the whole spectrum of folk, so I am in touch,” he said.

The Republican presidential contender, who has been surging in the polls, also said he owes nothing to Obama for breaking the White House color barrier. “I believe that even if President Obama had not been elected, it still would have been a non-issue,” Cain said. “I have experienced the decreasing significance or importance of color in this country, so it is not an issue at all.”

Cain also insisted he is not just a “flavor of the week candidate.”

“The answer is an emphatic ‘no,’” he said, “because Häagen-Dazs black walnut tastes good all the time.”

More from Cain, who campaigned in Concord, N.H., today.

On his rise in the polls:

“We have substance,” he said. “It is substance of ideas that is causing people to stay on the Herman Cain Train.”

Cain cited last month’s Presidency 5 straw poll in Florida as the turning point for his presidential bid, but emphasized his campaign doesn’t  “try to buy support; we earn support.”

On New Hampshire:

Cain, who was endorsed by several New Hampshire state legislators today, said he considers New Hampshire a “critical” state in the primary process.

“I will be back in Hampshire a lot over the next several weeks,” Cain said. He added, “Governor Romney has a significant lead right now, but that does not mean we’re not going to compete heavily here in this state.”

On a “two-person race”:

“I don’t think that it is a two-person race,” he said. “I think the people are going to decide that as time goes on. I’m happy to be up in the top tier with Mr. Romney.

“A lot of the national media have tried to make this a two-person race. You don’t know that. I got sick of seeing everything about the campaign being about Romney and Perry, not because I don’t like them, but I’m saying what are the rest of us, chopped liver?

“Message is more important than money.”

On why he hasn’t been out on the campaign trail more:

“The book tour is over.,” he said. “The book tour lasted five days and we still campaigned and did the book tour. We’re not on book tour. By the way, for the people who don’t know Herman Cain , I suggest you go buy a copy of ‘This Is Herman Cain.’”

On the future of his campaign:

“We currently have about 35 people full time on staff,” he said. “Some of them full time here in New Hampshire, some of them full time in Iowa, some of them full time down in Florida. We’ve got people out in Nevada, we’ve got people in South Carolina and then we’ve got a core of staff. We have run this very lean, by design. We are now going to ramp up. … As we speak, we are ramping up and filling some very valuable positions that we need to fill.

“We now have the money to do so. I didn’t want to get out in front and commit to spending a whole lot of money before I knew that the American people were going to say, ‘You know what, this long shot may not be such a long shot.’”

On Iran:

“The attempt on the part of Iran, and I do believe based upon reports that their fingerprints were all over this attempted assassination. I happen to believe that that is the direct result of Iran and other countries seeing America as weak,” he said. “When you present your nation or your leadership as weak, it invites attacks.

“This administration seems weak and some of its foreign policy moves have been very cloudy and foggy.”