The colloquial American-English phrase as busy as, or busier than, a one-armed paperhanger, and variants, mean exceedingly busy.
All the earliest occurrences that I have found of this phrase, and of similar ones, date from 1906.
Here they are, in chronological order:
1-: The phrase as busy as a one-armed man engaged in the exercise of bean-bag occurs in the following advertisement, published in The Pacific Commercial Advertiser (Honolulu, Hawaii) of Tuesday 19th June 1906:
THE FAVORITE GROTTO.
Our chef is kept as busy as a one-armed man engaged in the exercise of bean-bag. The reason is easily found. Today’s lunch menu, which follows, explains it:
SOUP—SCOTCH BROTH, BARLEY
CURRIED LAMB A LA BOMBAY,
GERMAN POT ROAST, POTATO
MASHED POTATO SPINACH
With Beer, Wine, Tea or Coffee.
Open all night.
F. J. KILEY, Prop.,
Cor. Hotel and Bethel Streets.
2-: The phrase as busy as a one-armed man engaged in the exercise of bean-bag occurs again in an advertisement for the same restaurant, published the following day in The Pacific Commercial Advertiser.
3-: The U.S. short-story writer O. Henry (William Sydney Porter – 1862-1910) used a phrase similar to as busy as a one-armed paperhanger in The Ethics of Pig, a short story about a man who practises “unillegal graft”, published in Munsey’s Magazine (New York—London: The Frank A. Munsey Company, Publishers) of October 1906:
I got as busy as a one-armed man with the nettle-rash pasting on wall-paper.
Illustration by E. M. Ashe for The Ethics of Pig—Munsey’s Magazine—October 1906:
4-: The earliest occurrence of as busy as a one-armed paperhanger that I have found is from Sunday Prizefight in Little Old New York. The Kind of “Sport” Indulged in Because Country Legislators Will Not Allow Legitimate Boxing in the Big Cities, by ‘Tad’, published in The Buffalo Enquirer (Buffalo, New York) of Monday 15th October 1906:
New York, Oct. 15.—Jeff O’Connell, an English featherweight, fought Charley Lucas, a New York lad, yesterday afternoon on a west side pier and battered him up in a fifteen round fight.
It was at 3 o’clock when the meeting was to take place. We all met in a bum saloon over on 8th Avanue [sic], somewhere near 37th Street, and waited for the mitt artists. There was a restaurant upstairs. A man with red grogans was the chef and he was as busy as a one-armed paper hanger with the hives.
5-: The second-earliest occurrence of as busy as a one-armed paperhanger that I have found is from Novices at Kicking. Americans Are Not the Champion Grumblers. Europeans Are Experts, by Clarence L. Cullen, published in The Evening Star (Washington, D.C.) of Saturday 20th October 1906—the author described
a Russian grand duke, a young man said to be worth some few hundreds of millions of dollars, a spender from away back, a man who on his tour of this country was as busy as a one-armed paper-hanger with the hives just tossing away money.
6-: An extended variant occurs in Letters From An Old Sport To His Son In College, by Jim Nasium, published in the Chattanooga Daily Times (Chattanooga, Tennessee) of Sunday 28th October 1906:
Dear Son—The bats in your garret must be flapping their wings again. If you hoop up with that gang of pikers to play professional football it’s bye-bye to the knowledge factory and back to the wheat belt for you. There’s something better ahead of you, and you just stay right where you are and keep busier than a one-armed philosopher with the itch working in a high wind.
Incidentally, in Letters From an Old Sport To His Son in College, published in the Chattanooga Daily Times (Chattanooga, Tennessee) of Sunday 28th April 1907, Jim Nasium wrote:
If you would succeed in baseball when you get on the field you want to keep busier than a one-armed paper-hanger with the hives.
7-: Finally, the following is from Split Finney Wonders Why They Do It. Will Some One Please Explain Why Men With Money Try to Break Their Necks?, published in The Sun (New York City, N.Y.) of Sunday 4th November 1906:
“Bo, as long as I’ve got a two piastre shinplaster in the kick or in sight I’m going to be as busy ducking trouble as a one-armed paperhanger with the hives.”