This was show-biz parlance in the 1920s, and it referred to a show that closed quickly after opening. The most famous usage was by Variety (a show-biz newspaper) in 1929 after the stock market crashed: "Wall Street Lays An Egg"
Some sources I have seen say that the original meaning came from the number 0, which is what is put up on a scoreboard when a team fails to score. It resembles an egg, and is still today called a "goose egg," so by extension when a team scores zero it "lays an egg."
I've got a use of "call shenanigans" that dates to 1998, and I strongly suspect that, even if it isn't the earliest use, it's the source of the phrase's popularity over the last decade or so.
In "Cow Days," the thirteenth episode of the second season of South Park, the boys are at a carnival playing games which they come to suspect are rigged. Kyle calls shenanigans, which brings Officer Barbrady to investigate. However, the carny allows the boys to win the game when the officer is present, and Kyle retracts his call of shenanigans.
Later in the episode, the boys discover that the prizes they were trying to win are in fact cheap knock-offs, and Kyle formally reinstates his claim of shenanigans. The claim is upheld this time by Officer Barbrady, which gives the townspeople free rein to destroy the carnival with brooms.
Again, this may not be the very first use of the term, but you asked whether anyone had made it particularly popular, and I think this is what did it. I saw the episode when it was new, and I remember quite distinctly thinking that I'd never heard the word shenanigans used that way before—but within days of the airing of that episode, several of my friends were calling shenanigans every chance they got.
Best Answer
The phrase "in so many words" means:
The phrase was already in use by 1674, in A supplement to the morning-exercise at Cripple-gate:
As to its exact origins, it is possible that there was a shift from the literal meaning "in as many words" in which so many became a reference to some unknown number. There is not, however, an article I could find which explains when or why this phrase came into existence.