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Bush addresses whether his brother's a problem for 2016

Last Updated May 30, 2015 8:25 PM EDT

It's not easy running a campaign for the White House -- especially if you're the brother and son of two of its former occupants.

But former Florida Gov. Jeb Bush's relation to former presidents George H.W. Bush and George W. Bush has proved to be both a boost to his early presidential poll numbers -- where name-recognition largely determines the outcome -- and a hindrance when it comes to policy questions.

During a stop in Tennessee, Jeb Bush sat down with "Face the Nation" host Bob Schieffer, who asked about the possible presidential candidate's relationship with his brother and the potential stumbling blocks it could cause in his own campaign.

When asked if he believed his brother was his main challenge, Bush told CBS News: "No, I don't."

Though the younger Mr. Bush has said that he poses a big threat to his brother's presidential aspirations, Jeb Bush put that notion to rest.

Still, the possible GOP contender acknowledged that "this is hard for me, to be honest with you."

"I have to do the Heisman onto my brother that I love. You know, this is -- this is not something I'm comfortable doing," Bush said. He went on to say that if he is a candidate, he will focus on his record as the governor of Florida.

"My brother's not going to be a problem at all. I seek out his advice. I love him dearly. I've learned from his successes and his mistakes," he said.

Bush recently came under fire for stumbling on whether he would have authorized the 2003 invasion of Iraq, a lasting legacy of his brother's presidency.

Republican presidential candidate and Kentucky Sen. Rand Paul knocked Bush for his "incredibly fumbled answer" to the Iraq war question, and even former Defense Secretary Robert Gates weighed in to say that Bush should not have been "trapped" by the issue.

Bush eventually clarified his position, saying he "would not have gone into Iraq" knowing the country did not harbor any weapons of mass destruction. But the incident has served as a reminder that the family name carries a weight that the current Bush in the national spotlight might still have to bear.

"I'm my own person, you know," the former Florida governor said. "I have my own life experience."