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According to a recently published Nixon biography, Nixon agreed somewhat reluctantly to the choice of Henry Cabot Lodge as his running mate in 1960, and quickly became disenchanted with Lodge. Apparently Lodge contributed little or nothing to the campaign whatsoever.
Now: I forget who was mentioned as possible alternatives, so we'll throw it wide open: whom else might Nixon have chosen, and what practical effect might that choice have had on the election? Granted, it's rare that the VP nominee gets much notice (the election of 1900 was a rare exception; see below) but in 1960, as close as it turned out to be, might someone other than the indolent Lodge have tilted the requisite handful of voters in key locations the other way?