I've read that in the June 1961 Vienna meeting between the two leaders that Khrushchev decided Kennedy was weak.
I've also read that this is bullshit and of the nature of an urban legend.
I am one of those who holds it was myth. To quote an old soc.history.what-if post of mine:
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IMO this is a myth. As Richard Ned Lebow and Janice Gross Stein wrote in
*We All Lost the Cold War*:
"The widely credited story that Khrushchev took Kennedy's measure in Vienna
and found him wanting originated with James Reston of the *New York Times.*
Three-and-a-half years after the summit, he proposed it as an explanation
for the Soviet decision to send missiles to Cuba. Reston was careful to
point out that his hypothesis was speculative and based on the president's
somber mood following his meeting with Khrushchev. [Elie] Abel and others
treated the proposition as an incontrovertible fact.
"All eyewitness accounts of the summit report plain speaking between the
two leaders with neither man giving ground. Arthur Schlesinger, Jr.,
described the conversations as 'civil but tough.' He insists that there is
no truth to 'the legend that Khrushchev browbeat and bullied Kennedy at
Vienna.' Kenneth O'Donnell, a political and personal confidant of the
president, tells the same story, as do Dean Rusk and knowledgeable Soviet
officials like Ambassador Georgiy M. Kornienko, who ridicules the notion of
Kenneday as a weak president. That 'doesn't fit at all with my impression
of how Khrushchev perceived Kennedy.'
"Khrushchev told reporters that Kennedy was tough, especially on the
question of Berlin. He confided to Kornienko that he had been right in his
assessment of Kennedy as a 'really intelligent, extraordinary politician.'
According to Sergei Khrushchev, 'Father returned to Moscow after the summit
with a very high opinion of Kennedy. He saw him as a worthy partner and
strong statesman, as well as a simple, charming man to whom he took a real
liking.' Speaking of the summit in his memoirs, Khrushchev remembered
Kennedy as a refreshing change from Eisenhower because of his thorough
preparation, frankness, and the verve with which he argued his case. 'This
was to his credit and he rose in my estimation at once. . . . He was, so to
speak, both my partner and my adversary.'"
http://books.google.com/books?id=Eaws3G98Ji0C&pg=PA71 (One thing that
impressed Khrushchev: Kennedy never consulted Rusk during the meetings as
Ike had consulted Dulles.)
(Lebow and Stein also argue that Khrushchev's decision to send missilies to
Cuba was "not the result of his low estimate of Kennedy's resolve; rather,
he decided to deploy them secretly out of respect for that resolve."
http://books.google.com/books?id=Eaws3G98Ji0C&pg=PA5 )
Likewise, Anna Tusa in *The Last Division: A History of Berlin, 1945-1989*
after noting Khrushchev's tribute to Kennedy's "precisely formulated
opinion on every subject," observes that "On reflection, Khrushchev can
hardly have been entirely pleased with the results of their meeting,
however enjoyable it might have been to score off the President for a
couple of days. His adversary had shown no signs of sympathy for his own
version of peaceful coexistence and no desire to turn Cold War swords into
ploughshares to aid Soviet technology and trade. He had failed to lure
Kennedy into negotiations over Berlin, by which he could have caused
ructions in the western alliance and weakened the allied position in the
city. He had issued a new ultimatum and, since his threats were beginning
to sound unconvincing to many friends and foes alike, he might have to act
on it and take major political and military risks. And it is probably true
to say that Khrushchev had made a serious miscalculation at Vienna. He had
made Kennedy's blood run cold, but after the initial shock the President
rallied and resolved to confront Khrushchev in Berlin..."
http://books.google.com/books?id=hlGVrPoOnRkC&pg=PA243
As Tusa notes, there is a curious divergence between the fact that
Khrushchev seems to have been impressed by Kennedy, and Kennedy's own
perception of the meeting. Kennedy was--even reading the transcripts weeks
after returning to Washington--"still shocked by Khrushchev's brutality,
though if he had compared his own experience with those of other victims,
he might have drawn the conclusion that Khrushchev had been almost
temperate by Kremlin stndards..."
If one chooses to disbelieve all these accounts rejecting the notion that
Khrushchev thought that JFK was weak, couldn't stand up to a confrontation,
etc., there is one other obvious argument against the idea: after Vienna,
Khrushchev once again did not follow through with his threat to sign a
separate peace treaty with East Germany. Instead, he built the Wall--
obviously an affront to the West (and to ordinary human decency) but
nevertheless in Khrushchev's view the least he could do to assure the
preservation of the GDR, and less likely than a separate treaty (which
would end the West's transit rights to Berlin) to provoke a war-threatening
crisis.
https://groups.google.com/d/msg/soc.history.what-if/ldbkcVUC8wM/HCiEOFH6aTcJ