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In June, Mr. Clinton caused the Obama campaign to go off message by endorsing GOP tax cuts for even the wealthiest wage earners. He later apologized, saying he was mistaken about the timing of congressional action needed to stave off tax increases.

The former president also poses a challenge for Mr. Biden’s role in the campaign because of Mr. Clinton’s unquestionable star power in the Democratic Party, as well as that of his wife, Secretary of State Hillary Rodham Clinton. It was telling that Democrats have given Mr. Clinton his own night to speak at their party convention in Charlotte, N.C., in September, while Mr. Biden must share the stage with Mr. Obama on the final night of the convention.

“The Obama campaign has a very, very deep farm team,” Mr. Johnson said. “There’s Barack Obama, you’ve got Michelle Obama, you’ve got Hillary Clinton and Bill Clinton. So Biden’s fifth on that list.”

Whether he is No. 2 or No. 5 on Mr. Obama’s list of surrogates, Mr. Biden is valued as someone who can connect with blue-collar, Reagan Democrats better than his boss. His roots in Scranton, Pa., give him the credibility to campaign in key battleground states such as Ohio, Pennsylvania, Iowa, Michigan and Wisconsin.