Actually not entirely true. When the U.S. originally started building nuclear weapons, the Soviets didn't have them and were not predicted to have them for years down the road (when they detonated their first it was quite the shock). Thus U.S. policy makers saw the role of nuclear weapons as "deterring" a Soviet conventional attack into Western Europe. Allowing the U.S. to maintain a relatively small (and cheap) conventional military. President Eisenhower himself was very much in favor of the policy of "massive retaliation" that is "they set one foot into West Germany, we vaporize all their cities".