“They told me if I voted for Goldwater, he would get us into a war in Vietnam. Well, I voted for Goldwater and that's what happened.”
This appears to be a variant of a widely disseminated Republican joke with no published attribution of its authorship to Buckley.
Mark Hatfield, as quoted in The Condition of Republicanism (1968) by Nick Thimmesch, p. 65
They told me if I voted for Goldwater we'd be at war in Vietnam in six months — and I did and we were.
Anonymous voter, as quoted in It All Comes Back to Me Now : Character Portraits from the "Golden Apple" (2001) by William O'Shaughnessy, p. 85
Buckley did say this on the Firing Line episode "Vietnam: Pull Out? Stay In? Escalate?" According to the transcript here http://hoohila.stanford.edu/firingline/programView2.php?programID=22, he says "...if someone told me that if I voted for Goldwater, we would escalate the war, I did and we have."
Misattributed
Variant: They told me if I voted for Goldwater in 1964, that we'd have more war and higher prices. Well, I did, and we do.
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William F. Buckley Jr. 43
American conservative author and commentator 1925–2008Related quotes

2000s, Where the Right Went Wrong (2004)

"Fethullah Gulen: Powerful but reclusive Turkish cleric", 2014
Source: The Fight for Democracy – The Libertas Voice in Europe. (2009), p. 46

Republican Convention Speech, 2004.
2003–2007 Governor of Massachusetts

During the general election of July 1865 where the Chartist Rowcliffe voted for a Conservative and another Liberal in order to oust Palmerston from the two-member constituency; quoted in F. J. Snell, Palmerston's Borough (Tiverton, 1894), pp. 107-112.
1860s
“People get what they vote for.”
2010s, 2017, Interview with Bill Kristol (2017)

Account of speech to a group, in Had enough?: A handbook for fighting back (2003), p. 2 http://books.google.com/books?id=gH4bMmu4CA4C