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Mr. Cleaver said Mr. Romney should take a page from the campaign playbook of 2008 Republican presidential nominee John McCain, who refused to give credence to conservative conspiracies that Mr. Obama was born outside the United States.

“You’re not going to attract African-Americans by getting [former Secretary of State] Condoleezza Rice, or three or four black people at a convention to speak, or making sure that when Mr. Romney speaks that he places an African-American in camera view,” he said. “That’s not it. It’s the policies” that matter.