“When you get to the end of your rope, tie a knot in it and hang on” is a saying that has been printed on many images. The saying has been cited in print since April 3, 1919, when this was printed in Life, a New York City-based humor magazine:
 
“WHEN one reaches the end of his rope, he should tie a knot in it and hang on.”
   
Thomas Jefferson (1743-1826) has been credited with the saying since the 1990s, but Jefferson never said it. Franklin D. Roosevelt (1882-1945) has been credited with the saying since at least 1958; he might have said the popular line, but there is no evidence that he said it first.
 
   
Monticello.org
Quotation: “When you reach the end of your rope, tie a knot in it and hang on.”
Variations:
“If you reach the end of your rope, tie a knot in it and hang on.”
“When get to the end of your rope, tie a knot in it and hang on.”
“When you think you have reached the end of your rope, tie a knot and hang on.”
(...)
Earliest known appearance in print: 1923
Earliest known appearance in print, attributed to Thomas Jefferson: 1996
 
HathiTrust Digital Library
3 April 1919, Life (New York, NY), pg. 585, col. 1:
WHEN one reaches the end of his rope, he should tie a knot in it and hang on.
   
17 April 1919, Buffalo (NY) Commercial, pg. 4, col. 4:
When one reaches the end of his rope, remarks Life, he should tie a knot in it and hang on.
 
16 January 1920, Daily Ardmoreite (Ardmore, OK), pg. 8, col. 6 ad:
WHEN
You get to the end of your rope, tie a knot in it and hang on!
(M&C Auto Supply Company.—ed.)
 
17 November 1922, Bessemer (MI) Herald, pg. 7, col. 3:
When you get to the end of your rope, tie a knot in it—and hang on.
 
30 November 1922, Perry (OK) Republican, pg. 8, col. 4:
Bill Whistle says when you get to the end of your rope, tie a knot in it and hang on.
 
13 May 1923, Trenton (NJ) Sunday Times-Advertiser, “Musings” by John H. Sines, pg. 8, col. 1:
“When you get to the end of your rope, tie a knot in it and hang on.”
 
17 June 1923, The Times-Picayune (New Orleans, LA), “See Big Field for Women in Dependency Prevention,” sec. 3, pg. 9, col. 2:
She must communicate something of this spirit to the workers meeting in the agents’ room hung with charts outlining results to be expected from five interviews (not calls) a day, and optimistic aphorisms like, “When you come to the end of your rope, tie a knot in it and hang on.”
 
6 March 1958, Evening World-Herald (Omaha, NE), ‘So They Said,” pg. 32, col. 2:
When you get to the end of your rope, tie a knot and hang on.—Franklin D. Roosevelt.
 
Google Books
Chicken Soup for the Breast Cancer Survivor’s Soul:
Stories to Inspire, Support and Heal
By Jack Canfield, Mark Victor Hansen and Mary Olsen Kelly
New York, NY: Open Road Integrated Media
2012
Pg. ?:
When you get to the end of your rope—tie a knot in it and hang on.
Eleanor Roosevelt
 
Google Books
Stock Trader’s Almanac 2015
By Jeffrey A. Hirsch
Hoboken, NJ: John Wiley & Sons, Inc.
2015
Pg. 77:
When you get to the end of your rope, tie a knot and hang on. — Franklin D. Roosevelt (32nd U.S. President, 1882–1945)
 
Twitter
Historical Quotes
‏@warsonapoleon
“When you reach the end of your rope, tie a knot in it and hang on.” - Thomas Jefferson
4:58 PM - 10 Jul 2015