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!"