I heard a snippet of the tape on the TV news, with some TV anchor commentary,
and it seems that while Jack Kennedy
indeed wasn't interested in space-exploration per se,
as an adventure or for its potential
resources, he was interested in "beating the Russians to the moon before the 1970's, and to make it the number-one priority for NASA."

Onm the other hand, Mr. Webb, in 1962, wasn't interested in making Project Apollo the number-one priority for NASA in the 1960's...
Mr. Webb feared that a manned space disaster would result if NASA was
rushed to send a man to the moon as
quickly as possible, and he feared
a public relations disaster would result for NASA.
Mr Kennedy overruled Mr. Webb's caution.

It's interesting to note what would have happened if Mr. Webb had got his way with Kennedy: NASA could have
taken a more cautious approach that
would have lead to the first moon landing in 1972, instead of 1969...
And the Soviets could have beaten America by sending the first cosmonaut
to circumnavigate the moon in 1969.
It's also interesting to speculate
if the Skylab hasd been sent up in
1976, instead of 1973.

Jacob