well in 1960 the moderates are strong in control of the party, they've had the White House for 8 years and their boy Ike is popular still with the people so if Barry is to win he needs a moderate or liberal to tack on as Veep, my guess is OTL's moderate-Liberal for 1960 Henry Cabot Lodge, Jr. or leader of the Liberals Nelson Rockefeller, liberal Prescott S. Bush would be a name to look at too