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“You look at all those supposedly vice presidential short-list invitees and not one, except maybe for Rob Portman, would bring enough to the ticket for Mitt to pick him,” said this Republican, who has ties to the campaign.

But some influential Republicans said there were substantive and practical reasons why Mr. Romney should look elsewhere for a running mate.

Romney will need to have control of the House and the Senate to right this economy,” said Republican National Committee Vice President Ruth Ulrich. “I would think Sen. Rubio would be much more valuable where he is. That is what is nice about building a strong farm team.”

And some even suggest Mr. Rubio himself, looking at poor track records of past vice presidents who later made a run for the Oval Office, may recognize a call from Mr. Romney is not in his best long-term political interests.

Said GOP strategist Paul Erickson, “The road from Observatory Hill [the official Washington residence of the vice president] to the White House is lined with the corpses of vice presidents who ignored history.”