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"Look, if this election is about Barack ObamaBarack Hussein ObamaThe Memo: The Obamas unbound, on race Obamas' first White House dog, Bo, dies Census results show White House doubling down on failure MORE's policies and the results of those policies, Barack Obama is going to lose," Barbour said. "Any other issue that gets injected to the campaign is not good for the Republicans. Republicans should want this election to be what American presidential elections have always been: a referendum on the incumbent's record. Barack Obama cannot win a second term running on his record. Zero chance. So anybody who talks about anything else is off-subject."

Perry called the issue a “distraction” himself earlier on Tuesday, while also telling CNBC “it’s fun” to taunt Obama on the issue.

"I don't have a clue about where the president — and what this — birth certificate says. But it's also a great distraction. I'm not distracted by it," Perry said.

Perry is credited with reigniting the so-called "birther" controversy, a movement that questions Obama's legitimacy to serve as president by casting doubt on his place of birth. The controversy seemed to die down following the release of his long-form birth certificate in April, but Perry brought up the subject in a profile with Parade magazine published over the weekend.

Both Barbour and Bush are high-profile Republican politicians who have been named as possible presidential contenders. Both rejected the idea of a bid for the nomination in 2012. Either of their endorsements would be a huge “get” for any of the Republican candidates.