A new Republican Party President was only elected later in the following decade of the early 1950s with the losses by two-time nominee , the Governor of Illinois Adlai Stevenson II ( grandson of the Adlai Stevenson I of the 1892 United States presidential election ) to the very popular war hero and commanding general in World War II , General Dwight D. Eisenhower ( in 1952 United States presidential election and 1956 United States presidential election ) .