This article is from the alt.usage.english FAQ, by Mark Israel email@example.com with numerous contributions by others.
This is now a very common phrase, as a search of Deja News
will show. But Merriam-Webster reports that it has no citations of
the whole phrase earlier than 1988, and no citations of "turnip
truck" earlier than 1985. R. J. Valentine writes: "This phrase
has been used for many years by Johnny Carson, who hosted "The
Tonight Show Starring Johnny Carson" on NBC from the early 1960s to
the early 1990s. He used it in precisely in the context discussed.
He may not have originated it, but he certainly popularized it, and
began doing so long before 1985."
Evan Morris, at <http://www.interport.net/~words1>, says that
this phrase "seems to be a good example of an entire class of catch
phrases based on urban-rural rivalry. The thrust of such phrases
is, of course, that 'I am not a fool or a newcomer,' and, in this
case, that 'I am not an ignorant country bumpkin who just arrived in
the big city on a truck full of lowly turnips that I was dumb
enough, on top of everything else, to fall off of.' This image of a
bewildered hayseed ripe for fleecing by urban con artists is a
close relative of more general phrases used to assert one's 'insider
status' and thus intelligence or savvy. The United States being a
nation largely composed of immigrants, it's not surprising that the
all-time most commonly heard phrase of this type is 'I didn't just
get off the boat.'"