...or, it may not. You'd have to be well over thirty to remember National Airlines (not to be confused with a cargo and charter carrier based in Ypsilanti, Michigan), which was founded in 1934 and merged into Pan American World Airways in 1980. Pan Am went into bankruptcy and ceased operating in 1991. In its heyday, National was strong on two routes: the East Coast route from the Northeast to Florida, and the Southern Tier transcontinental route connecting Florida, Texas, and California.
As this Time article reported, some flight attendants (then commonly called "stewardesses"--male attendants were rare in those days) objected to this campaign; in particular, to the company's requirement that they wear "fly me" buttons on their uniforms. The article quotes National's PR director: "We had no preconceived idea of injecting a suggestive leer into the campaign." Um-hmmm.
According to one of the comments on the "I'm Maggie, Fly Me" video, the campaign was the brainchild of Dick Wolf, who went on to create the TV series Law and Order.
Thanks to stantonz for the "Miami Go Go" clip (and to FB friend Georgene Z. Russell for bringing it to my attention), and to HalfordJetset for the "Fly Maggie" clip.