It would have been cool if it was Senator Margaret Chase Smith.
A very interesting pick. Republican Party would be far ahead of its time by naming a woman to a national ticket of a major party.
Other possibilities
Senator Prescott Bush from Connecticut. This would have been another feather in the cap for the Bush dynasty.
Senator William Knowland from California. The pick of Knowland would have been a slap in the face for Nixon as Knowland and Nixon were rivals for influence in the California Republican Party. Knowland was in fact considered for VP by Eisenhower in 1952, but ultimately decided on Nixon.
Governor George Craig of Indiana. Sided with the Eisenhower wing of the party in 1952.
Herbert Brownell, U.S. Attorney General in Eisenhower cabinet. Brownell was very trusted by Eisenhower and was extremely helpful to Eisenhower especially in domestic policy. He as well helped Eisenhower speed up desegregation in the South. As a result, Brownell did not go over well with large segments of the population in the South, so this would likely have hurt Eisenhower in the south in the election. However, the selection of Brownell would have said to the South and to the nation that we are doing what is right, not what is politically expedient. This may have increased his support even more in the states outside the South. The Democrats won most of the deep South in 1956 anyway, so it would not have had any effect on another Eisenhower landslide victory anyway.
