“A committee is a group of the unwilling, appointed by the unfit, to do the unnecessary” is a joke about committees that has been cited in print since at least 1952. The words “unwilling” and “unfit” are sometimes switched in the saying, but the original formation makes the most sense (“unfit” can appoint “unwilling,” but “unwilling” usually doesn’t appoint “unfit”).
 
The radio and television journalist Richard Harkness (1907-1977), the Washington correspondent for NBC from 1943-1970, is frequently given credit for this saying. However, Harkness’s cited use is from the New York (NY) Herald Tribune of June 15, 1960—far later than the earliest 1952 citation.
 
     
The Quote Garden
Quotations about Committees & Meetings
A committee is a group of the unwilling chosen from the unfit, to do the unnecessary.  ~Author Unknown
 
Google Books
Industrial Hygiene Digest
Volume 1; Volume 17
1953
Pg. 31:
And now we have a new definition of a committee: “A committee is a group of the unwilling, appointed by the unfit, to do the unnecessary.”
—Detroit Medical News, Dec. 8, 1952
     
Google Books
Public Works
Volume 84
1953
Pg. 115:
There are many jokes about committees, like: “A committee is a group of men who individually can do nothing but as a group can decide that nothing can be done” — or — “A Committee is a group of the unfit, appointed by the unwilling to do the unnecessary.”
 
31 July 1954, Oneonta (NY) Star, “The Gunny Sack” by Corald (Gunny) Gunthrup, pg. 4, col. 4:
The Gunny Sack: The office wit telling us that a committee is a group of unfit appointed by the unwilling to do the unnecessary.
   
27 September 1955, Bradford (PA) Era, “Round the Square,” pg. 1, col. 1:
DEFINITIONS: (...) Committee—A group of the unfit, appointed by the unwilling, to do the unnecessary.
   
Google Books
Humorous English;
A guide to comic usage, jocular speech and writing, and witty grammar
By Evan Esar
New York, NY: Horizon Press
1961
Pg. 62:
A committee is a group of the unfit, appointed by the unwilling, to do the unnecessary.
 
Google Books
The Modern Handbook of Humor
By Ralph Louis Woods
New York, NY: McGraw-Hill
1967
Pg. 8:
A committee is a group of the unfit, appointed by the unwilling, to do the unnecessary.
 
Google Books
Business Governance Handbook:
Principles and Practice
By John W Hendrikse and Leigh Hendrikse
Cape Town: Juta Academic
2004
Pg. 288 (Chapter 22 Board Committees):
What is a committee?
A group of the unwilling, picked from the unfit, to do the unnecessary.
Richard Harkness, New York Herald Tribune, 15 June 1960