In this cartoon-within-a-cartoon, Bugs and Elmer are in the midst of their usual hunting-chasing scenario. After Bugs tricks Elmer into running through a hollow log and off a cliff three times (a comic triple of sorts originally used in Avery's All this and Rabbit Stew. In fact, the same animation sequence was recycled for "The Big Snooze", with the stereotypical black hunter being redrawn into Elmer Fudd), Elmer becomes enraged and frustrated that the writers never let him catch the rabbit in the pictures they both appear in. He tears up his Warner Bros. cartoon contract and walks off the set to devote his life to fishing, stunning Bugs, who piteously protests and effortlessly tries to ask him to reconsider. During a relaxing fishing trip, Elmer falls asleep.
Bugs observes Elmer's nap and takes sleeping pills in order to rock Elmer's "dreamboat" (Bugs sang Beautiful Dreamer, by "invading" his dream and continuing to drive Elmer crazy when Bugs uses the "Nightmare Paint". Symbolic of his dreamland plight, Elmer appears nearly nude, wearing only his derby hat and a strategically placed "loincloth" consisting of a laurel wreath. Elmer's dream is invaded by "ziwwions and twiwwions of wabbits" dancing on his head and singing "The rabbits are coming. Hooray! Hooray!" in a musical parody of "The Campbells Are Coming" and a visual parody of the Pink Elephants on Parade sequence from the 1941 Disney film Dumbo with Bugs Bunny literally multiplying them from an adding machine. Looking for another way to torment Elmer, Bugs consults the book A Thousand and One Arabian Nightmares, exclaiming, "Oh, no! It's too gruesome!" before peeking over the book to cheerfully tell the audience, "But I'll do it!" Elmer realizes what Bugs has in mind, pleading "No, no! No, not that! Not that, pwease!" as Bugs ties him to railroad tracks, just as "the Super Chief" (Bugs in an Indian chief's war bonnet, leading a conga line of baby rabbits) crosses over Elmer's head.
Elmer's anger at a failed pursuit through the surreal landscape, down connected rabbit holes, is promptly used against him by Bugs who inquires "What's the matter doc, ya cold? Here, I'll fix dat". Before Elmer can protest, Bugs dresses him like a woman by wrapping his body with green material from the right, slapping a wig on him, and applying lipstick. Bugs inspects his handiwork, then lifts the backdrop to reveal a trio of literal wolves in Zoot suits, lounging by the sign at Hollywood and Vine. When the trio notice Elmer, one wolf howls, "Hooooow old is she?" while another begins flirting with Elmer. Bugs enjoys watching the male wolves hit on Elmer, who yells "Gwacious!" before grabbing the hem of his gown and fleeing from the pursuing wolves, briefly stopping to ask the audience, "Have any of you giwls evew had an expewience wike this?"
In an attempt to "help," Bugs persuades Elmer to make a mad dash towards stage right, as Bugs plays the old "run 'this way'!" gag, putting Elmer through a bizarre series of steps which include running on his feet, flipping upside down to run on his hair, hopping on all fours, and dancing a hopak.
As Bugs and Elmer dive off a cliff, Bugs drinks some "Hare Tonic (Stops Falling Hare)" and screeches to a halt in mid-air, while the dream Elmer continues to careen toward earth, finally crash-landing into the real Elmer's snoozing body as he wakes up with a start, exclaiming "Ooh, what a howwible nightmare!".
Elmer dashes back to the cartoon's original set, pieces his Warner contract back together, and agrees to finish what he started. The chase through the log begins anew. Bugs faces the audience in a closeup, closing with the catchphrase from the "Beulah" character on the radio show Fibber McGee and Molly, "Ah love dat man!"
The Big Snooze is available in a restored, uncensored version on the Looney Tunes Golden Collection: Volume 2 DVD set, and as part of the compilation What's Up, Doc? A Salute to Bugs Bunny on Volume 3.