Very drunk, specifically on
gin.
A result of the "gin craze," British government tried to stem the flow of gin with prohibitive taxes and rules, which drove the gin scene underground during
18th-century England. Exploiting a loop-hole in these new regulations, where a bartender couldn't be
prosecuted for serving gin if the police couldn't be sure exactly which bartender served it, wooden plaques shaped like a black cat (hence "Old Tom gin") were mounted on the outside wall of some pubs. These cat plaques had little paws, and
under the cat's paw was a slot to put money in and a small lead tube. From the tube would come a shot of gin, poured by the bartender, who remained anonymous from inside the pub.
Today, "under the cat's paw," simply means to be very drunk on gin, perhaps to great excess, as that is where most of these gin-crazed bar-patrons would have spent most of their time.
"I'm going to be
under the cat's paw tonight!"
"Billy, if you don't slow down on those martinis, you'll be under the cat's paw
in no time!"
"
I can't remember a thing- I was absolutely under the cat's paw!"