In my mind, the foundational claim of Kennedy's Inaugural Address is to awaken Americans to the sense of change he envisioned his administration to usher.  The claim is made repeatedly in terms of how his government is to act and how Americans should respond to it.  The most famous lines of the speech attest to this.  The significance of this is that President Kennedy felt that the best way to pivot in making his administration one that would be supported by the public was to create the mystique that it was going to be an agent of change in the world.  It very well might have been, but President Kennedy and his advisers understood that it was important to convey this to the public as soon as possible and enable them to understand that they were a part of this "living history" claim that President Kennedy was putting forth in his address.  This helped to make President Kennedy's Inaugural Address something that would be looked upon for so many people at so many different points in history as relevant and meaningful.  President Kennedy understood that the basic claim of constructing America as an agent of change in the world was the only way in which he felt Americans would be able to rally around his administration and lend to it the support he knew would be needed.