“The man who rows the boat generally doesn’t have time to rock it” (political proverb)

To “rock the boat” means to change or disturb an existing situation. “The man who rows the boat generally doesn’t have time to rock it” is a political proverb that means that a person in an existing political situation (such as an elected member of the Republican or Democratic parties) doesn’t change that situation.
 
“The man who rows a boat generally doesn’t have time to rock it” has been cited in print since at least 1922 or 1924.
 
     
The Free Dictionary
rock the boat
1. Lit. to do something to move a boat from side to side, causing it to rock. (Often in a negative sense.) Sit down and stop rocking the boat. You’ll turn it over!
2. Fig. to cause trouble where none is welcome; to disturb a situation that is otherwise stable and satisfactory. (Often negative.) Look, Tom, everything is going fine here. Don’t rock the boat! You can depend on Tom to mess things up by rocking the boat.
 
(Oxford English Dictionary)
fig. to rock the boat: to disturb the equilibrium of a situation; to stir up trouble. Cf. to make waves at wave n. 3d.
1903 A. H. Lewis Peggy O’Neal ii. 60   The worst that both of us might do of public evil would hardly serve to rock the boat.
1931 F. L. Allen Only Yesterday vi. 156   Unfortunate publicity had a tendency to rock the boat.
   
25 April 1920, Fort Worth (TX) Star-Telegram, “Pungent Paragraphs,” pg. 6, col. 6:
Mr. Gompers says: “This is no time to rock the boat.” When, then, is the proper time to rock it?—Providence Tribune.
   
Google Books
Telephony
Volume 82
1922
Pg. 194:
It has been said: “The man who rows a boat generally doesn’t have time to rock it.”
 
19 June 1924, Rockford (IL) Republic, “Hit and Run,” pg. 8, col. 2:
Man who rows the boat has no time to rock it.
 
Google Books
Modern Eloquence, founded by Thomas B. Reed:
supplementary volumes, volume 3

By Thomas B. Reed. Ashley Horace Thorndike. Brander Matthews, Robert Laird Borden, et al.
New York, NY: Modern Eloquence Corp.
1927
Pg. 266:
The man who rows the boat has no time to rock it.
     
24 October 1940, Port Arthur (TX) News, pg. 9, col. 5 ad:
CY COLOGY SEZ:
“The Man Who Rows the Boat Has No Time to Rock It.”
(Builders Lumber Co.—ed.)
 
21 February 1949, Trenton (NJ) Evening Times, pg. 14, col. 6:
“The man who rows a boat generally doesn’t have time to rock it.”—Delco Doings.
 
Google News Archive
10 July 1951, The Telegraph-Herald (Dubuque, IA), “Star Dust,” pg. 2, col. 1:
A man who rows a boat generally doesn’t have time to rock it.
—Col. Starbottle
     
Google News Archive
30 June 1955, Calgary (Alberta) Herald, “Scrap Book” by Shelagh Nolan, pg. 4, col. 3:
The man who rows the boat generally doesn’t have time to rock it.
   
Google Books
Mediation:
Empowerment in Conflict Management

By Kathy Domenici
Prospect Heights, IL: Waveland Press
1996
Pg. 112:
The banner over the owner’s desk reads, “The man who rows the boat doesn’t have time to rock it.” The message coming from the owner is to keep the momentum but not to sacrifice any employees.