[QUOTE=RickJay]
I don’t mean for this to sound rude, but given the realities of human memory and how events since an event can change perception of that event, I’m going to up and question the notion that JFK was an inspirational President. His administration was short, unimpressive in terms of accomplishments even given its shortness, and was not particularly noted for being a time of unusual optimism. I would in fact suggest that the administration of Dwight Eisenhower, which immediately preceded Kennedy’s, was probably THE all-time high point of American optimism.
Kennedy has been deified in large part because he was assassinated, giving him the status of martyr. His words have been elevated above their perception at the time because no more words could be had from him after his death. He was certainly not any more popular than most Presidents as these things go prior to November 22, 1963.
[/QUOTE]
Remember 50-mile walks? 
I would submit that anyone who could get so many Americans to try to walk fifty miles in one day is by their very definition exceedingly inspirational.
But perhaps I should define what I meant by mentioning Kennedy along with Reagan in terms of being inspirational, as they were inspirational in different ways. Reagan had the ability to re-instill pride in being American, and to make people optimistic about the future (which was exactly what the country needed following the doldrums caused by the Carter administration).
Kennedy, rather than being inspirational to the country about its future (although in certain ways he was), was inspirational to people on a personal level. He was young, handsome, vigorous and charismatic (this last being a de facto requisite, IMO, to being inspirational in the first place). He got people interested in physical fitness (the 50-mile walk being one example, the touch football craze being another) and in sacrificing time and effort of their own in service to others (the Peace Corp). He was cheered by adoring crowds wherever he went, even abroad (helped in no small part here by his adoringly beautiful, charming and stylish wife).
On the national level, like you say, he didn’t have time to accomplish much - though I do recall that his inaugural reading of “Ask not…” made quite a significant impact even at that time. He was inspirational in terms of getting people behind the space program with his declaration that we would put a man on the moon within a decade, and I believe that his embracing of and support for the civil rights movement made the transition go more smoothly than it might have otherwise (not that it went all that smoothly to begin with, but I do believe that his having backed it made a significant segment of the population take a second look at their own view regarding racial equality).
Both Kennedy and Reagan brought a Hollywood-style glamour to the White House. Whereas people like to call Clinton a rock star president, Kennedy was a movie star president, and this also, I believe, played into his ability to get people to like and support him.
And a side note, people gained an even greater appreciation of him once the scary Cuban Missle Crisis was over. People felt at the time that Khrushchev thought he could take advantage of Kennedy’s youth and inexperience (and IMO, the fact that he was a Democrat (:D) and that they hadn’t tried it with [General] Eisenhower in office) to get away with installing and aiming nuclear weapons at us from ninety miles offshore, and Kennedy backed him down. Now I will grant that this doesn’t go so much toward inspirational ability, but it did grant him a certain gravitas and it earned him a great deal of respect from quarters where he didn’t necessarily have it before.