Turns out "hearts and minds" didn't originate with the Vietnam War but, according to wikipedia, with John Adams, the American Revolutionary War patriot and second president of the United States.
In Adams's letter of February 13, 1818, he wrote:
"The Revolution was effected before the War commenced. The Revolution was in the minds and hearts of the people;
a change in their religious sentiments of their duties and obligations.... This radical change in the principles, opinions, sentiments, and affections of the people, was the real American Revolution".
That's its American roots, anyway. No doubt people figured it out long ago, too.