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Mr. Rubio released his memoir, “An American Son,” and was widely considered to be on the short list of potential running mates for Mr. Romney. He didn’t get the nod, but he delivered a well-received speech at the Republican National Convention.

The presidential exit polls immediately shifted the attention back to Mr. Rubio, as Mr. Obama steamrolled Mr. Romney among Hispanics and young voters, while Mr. Romney outperformed Mr. Obama by smaller margins among white voters and those older than 65.

Mr. Cardenas, though, warned that the party must be careful not to “pigeonhole” Mr. Rubio “into a demographic need.”

“If we do that, we are really diminishing his appeal to a broader electorate, and that would be unfair to him,” he said.

Others agree.

Rubio’s attractiveness as a candidate and as a conservative leader is anchored in his support for conservative principles, not his ethnicity,” said Morton Blackwell, one of Virginia’s two Republican National Committee members.

“The Lord did not give all talents to everybody, but he certainty gave a double-helping of charisma to Marco Rubio.”