A few X short of a Y
This Spoken English - Namrata Palta · 2006
Not possessing all of one's mental faculties; crazy, stupid
In these phrases, X is a common component of Y. Y represents full mental capacity, and the lack of a few X implies a lack of full mental capacity...
. a few fries short of a happy meal
. a few sandwiches short of a picnic
. two bricks short of a load
. a few syllables short of a Haiku
. a couple of cans short of a six-pack
I suspect the basic trope has only been around (or at least, only widespread) for a few decades. The nearest written version of OP's example I could find was...
a few trombones short of a brass band
...from a 1998 British stage review publication. But several of those "typical" examples suggest an Australian origin to me, and if this NSW Public Schools Millennium Marching Band is anything to go by, marching bands are still alive and kicking down under!
It's partly the fact that there are so many variations that makes me think it's "recent" (so still "novel"). Here's a bunch more from The Mammoth Book of Insults - Geoff Tibballs · 2011...
He's a few trees short of an orchard
He's a few clowns short of a circus
He's a few peas short of a pod
He's a few currants short of a fruit cake
He's a few guppies short of an aquarium
He's a few flowers short of an arrangement
He's a few spokes short of a wheel
He's several nuts short of a full pouch
He's a few chapters short of a novel
He's a few pancakes short of a stack
He's a couplet short of a sonnet