Claude A. Swanson (1862-1939), Virginia’s U.S. Senator from 1910-1933, had a rule for new Congressmen that was published in Current Opinion in 1923: “When the water rises to the second deck, put on a life preserver and follow the rats.” Frank R. Kent’s book, Political Behavior: The heretofore unwritten laws, customs and principles of politics as practiced in the United States (1928), put Swanson’s rule into a more popular form: “When the water reaches the upper decks, follow the rats.”
 
Swanson’s rule means that you can stand on principle, but when the ship’s sinking and the rats leave the ship, it’s time to abandon the principle. It’s not known when Swanson first formulated the saying.
 
   
Wikipedia: Claude A. Swanson
Claude Augustus Swanson (March 31, 1862 – July 7, 1939) was an American lawyer and Democratic Party politician from Virginia.
 
He served seven terms in the U.S. House of Representatives, from 1893 until 1906, was the 45th Governor of Virginia from 1906 until 1910, and represented Virginia as a United States Senator from 1910 until 1933. Swanson lived most of his life at his estate Eldon in Pittsylvania County, Virginia, built by the Whittle family for whom Chatham’s Whittle Street is named.
 
He was Secretary of the Navy under Franklin D. Roosevelt from 1933 until his death at age 77.
     
Google Books
1 July 1923, Current Opinion, “The Colyumists’ Colyums,” pg. 104:
Among the visitors to Washington since Congress adjourned are many Congressmen-elect, installing themselves in the House Office Building and incidentally “learning the ropes.” One of them asked a veteran legislator for some pointers on how to make a success in Congress.
 
“I know of no better way,” was the reply, “than to follow the rules once laid down by Senator Swanson of Virginia to a bunch of new Congressmen:
 
“‘First. Work one day and then take six days off to talk about it.
 
“‘Second. Never take anything you can’t carry.
 
“‘Third. When in doubt, do right.
 
“‘Fourth. When the water rises to the second deck, put on a life preserver and follow the rats.’”
     
16 August 1924, Baltimore (MD) Sun, “Davis delayed in campaign by new machinery” by Frank R. Kent, pg. 1:
Nearly everybody else lived up to well-known proverb so often quoted the sage Senator from Virginia, Claude A. Swanson, as follows: “When water reaches the upper deck, follow the rats.”
 
27 March 1927, Cleveland (OH) Plain Dealer, pg. 7A, col. 3:
Of Senator Claude A. Swanson of Virginia:
 
“Unlike Glass, Swanson is always suave, and he is a consummate politician. He is a born horse trader. He is reputed to live by three mottoes: ‘When in doubt, do right,’ ‘When the water reaches the upper deck, follow the rats’ and ‘Be bold as a lion on a rising tide.’
 
Google Books
Political Behavior:
The heretofore unwritten laws, customs and principles of politics as practiced in the United States
By Frank R. Kent
New York, NY: W. Morrow
1928
Pg. 153:
When the Water Reaches the Upper Decks, Follow the Rats.
 
4 September 1928, Syracuse (NY) Herald, pg. 8, col. 3:
The rules of political success as Mr. Kent sets them forth are: (...) “When the water reaches the upper decks, follow the rats”—which means abandon any principle you have when it becomes unpopular;...