Many of American's views on socialism root back to the Cold War. It seems that the younger generation has embraced socialism much more than the preceding generations. There was a time when a fear of socialism could be rationalized, but now under a more-left America, socialism is not necessarily a radical concept. Despite this, many Americans, especially Republicans, seem to misunderstand the definition of socialism, and continue to dismiss it as "radical" or using "socialist" as a political insult. There are many people with socialist ideas who deny that they are "socialist" and look upon it as a dirty word. Many people continue to associate "socialism" with communism. The definition varies. Although the socialism that people like Bernie Sanders praise should be looked at in a positive way.
That I don't know too many people (that oppose Socialism) to know it's definition. The main reason Americans are afraid of it are because of the Red Scares, McCarthyism, and Black listing that plagued the United States in the 20th century. During these times, it was rational to fear socialism, because being associated with it meant that you could lose your job, your family could be starved, or that you could be found guilty of treason.