Extravagance can be intoxicating, and those who grow accustomed to extravagance, only to be deprived of it, can miss it terribly. That accounts for much of the powerful hold John F. Kennedy has on a generation of Americans even today. He led people to imagine that their government had the boundless capacity to improve the world, and on the day he died, they could still believe that.

His administration and that of his vice president and successor Lyndon B. Johnson are significant in the same way: They represent the pinnacle of ambitious, visionary government. What each president lacked was a sober sense of the limits of what it could do, at home or abroad.

For a while, their confidence infected the American people. But the course of history was to furnish an unpleasant antidote.

Kennedy came into office having roused unrealistic expectations. "With the coming of a new administration, something akin to religious fervor distracts most Americans, an extension of the endless quest for a future that has something more to offer," wrote biographer Herbert Parmet. "With Kennedy this spirit was compounded, exaggerated, made more irrational."

His inaugural address did nothing to dampen the mood. It cast the United States not just as the defender of its own security and freedom, but as guarantor for the entire planet. Kennedy declared that "we shall pay any price, bear any burden, meet any hardship, support any friend, oppose any foe, in order to assure the survival and the success of liberty (emphasis added)."

In case that promise did not seem sufficiently grandiose, he added, "The energy, the faith, the devotion which we bring to this endeavor will light our country and all who serve it—and the glow from that fire can truly light the world."

Kennedy gave the highest priority to the foreign arena. But Johnson's domestic program grew out of initiatives begun by JFK. And LBJ was no more inclined to restrain his rhetoric.

He extolled his social welfare plan as though he were describing paradise: "The Great Society is a place where every child can find knowledge to enrich his mind and to enlarge his talents. ... It is a place where the city of man serves not only the needs of the body and the demands of commerce but the desire for beauty and the hunger for community ... beckoning us toward a destiny where the meaning of our lives matches the marvelous products of our labor."

Neither president paused to consider whether and how the clumsy tools of government could actually fulfill these dreams. Kennedy took the first steps into a war in Vietnam—which proved that supporting friends did not assure the success of liberty and that there were some burdens Americans would not bear.

When Johnson signed the Economic Opportunity Act, he proclaimed that it represented nothing less than "a commitment to eradicate poverty." But biographer Robert Dallek wrote that the president "was clueless as to just how the program would work." Like many Great Society programs, it did not live up to its billing.

Neoconservative thinkers have long revered Kennedy for his belief in using military power to propagate democracy and human rights abroad, even in places where they were unlikely to flourish. There is a straight line from his inaugural address to our invasion of Iraq and our protracted presence in Afghanistan, both costly, high-minded adventures with meager payoffs.

JFK's domestic plans provided the inspiration for Johnson's Great Society, which likewise attracted plenty of overconfident intellectuals. "In 1962," wrote Dallek, "a group of University of Michigan social welfare experts predicted that it would be relatively easy to end poverty in America at a cost of $2 billion a year, less than 2 percent of GDP."

Today, we spend triple that amount, 6 percent of GDP, and poverty has yet to be ended. In 2012, the Census Bureau says, nearly 50 million Americans—16 percent of the population—were poor even after it counted the various forms of government aid they get.

JFK and LBJ set out to prove how much the U.S. government could accomplish at home and abroad, a mission that endeared them to those who believe in the promiscuous use of power. They ended up proving how much it could not accomplish, and how little extravagance can buy.