The title is a play on the phrase "punch drunk" alluding to the elephant's "trunk."
A five-inch-high elephant arrives at Pier 38 in New York City in a boatload of bananas. The city is paralyzed by what its residents take to be a mass hallucination.
A tiny elephant emerges from a banana boat and wanders about town, causing an uproar among the populace. Sightings are attributed variously to mass hysteria, insanity and dipsomania.