U.S. foreign policy during the Cold War era hinged upon a variety of factors which included strategic objectives, perceived threats to U.S. security, public support and partisan politics. One approach to understanding the complexity of this is to view, or review the crisis which erupted and came close to igniting a military confrontation between the US and the USSR in 1963 known as the Cuban Missile Crisis.
Your assignment is to trace the path of public perception beginning with the close of the Eisenhower administration’s handling of the Cuban Revolution ignited by Fidel Castro through the close of the Cuban Missile Crisis of 1963 and compare it to the reality behind those events. In other words you are to discover what during the Vietnam War era came to be called “the credibility gap,” the difference between what the administrations handling foreign policy knew and what the public was informed, not only by the administration but by the opposition party and candidates.
An excellent starting point is The National Security Archive although a search of the Web will reveal other sources which you may wish to consult.