“If nominated I will not accept/run, (and) if elected I will not serve” is the famous “Sherman statement” on declining to run for political office, but William Tecumseh Sherman (1820-1891) never used those exact words. Sherman issued this widely published statement in June 1871:
 
“I hereby state and mean all that I say, that I never have been and never will be a candidate for President, that if nominated by either party, I should peremptorily decline and even if unanimously elected I should decline to serve; if you can find language stronger to convey this meaning you are at liberty to use it.”
 
Sherman telegraphed the Republican National Convention in June 1884:
 
“I will not acceot if nominated, and will not serve if elected.”
 
Seth Low used the now-popular form in 1908, when asked if he’d run again for New York City mayor: “If nominated, I will not accept. If elected, I will not serve.”
 
 
WIkipedia: William Tecumseh Sherman
William Tecumseh Sherman (February 8, 1820 – February 14, 1891) was an American soldier, businessman, educator and author. He served as a General in the Union Army during the American Civil War (1861–65), for which he received recognition for his outstanding command of military strategy as well as criticism for the harshness of the “scorched earth” policies that he implemented in conducting total war against the Confederate States. Military historian B. H. Liddell Hart famously declared that Sherman was “the first modern general.”
 
Sherman served under General Ulysses S. Grant in 1862 and 1863 during the campaigns that led to the fall of the Confederate stronghold of Vicksburg on the Mississippi River and culminated with the routing of the Confederate armies in the state of Tennessee. In 1864, Sherman succeeded Grant as the Union commander in the western theater of the war. He proceeded to lead his troops to the capture of the city of Atlanta, a military success that contributed to the re-election of President Abraham Lincoln. Sherman’s subsequent march through Georgia and the Carolinas further undermined the Confederacy’s ability to continue fighting. He accepted the surrender of all the Confederate armies in the Carolinas, Georgia, and Florida in April 1865.
 
When Grant assumed the U.S. presidency in 1869, Sherman succeeded him as Commanding General of the Army (1869–83). As such, he was responsible for the U.S. Army conduct in the Indian Wars over the next 15 years, in the western United States. He steadfastly refused to be drawn into politics and in 1875 published his Memoirs, one of the best-known firsthand accounts of the Civil War.
   
Wikipedia: Shermanesque statement
“Sherman(esque) statement” or “Sherman speech” is American political jargon for a clear and direct statement by a potential candidate indicating that he or she will not run for a particular elected position.
 
The term derives from the Sherman pledge, a remark made by American Civil War General William Tecumseh Sherman when he was being considered as a possible Republican candidate for the presidential election of 1884. He declined, saying, “I will not accept if nominated and will not serve if elected.” Thirteen years prior, he had similarly asserted, “I hereby state, and mean all that I say, that I never have been and never will be a candidate for President; that if nominated by either party, I should peremptorily decline; and even if unanimously elected I should decline to serve.” These statements are often abbreviated as “If drafted, I will not run; if nominated, I will not accept; if elected, I will not serve.”
 
Examples
President Lyndon B. Johnson famously invoked the pledge in his March 31, 1968, national address announcing that he would not seek a second full term, saying “I shall not seek, and I will not accept, the nomination of my party for another term as your president.”
 
Since then, journalists have often pushed for potential candidates to give a Sherman pledge in lieu of a less definitive answer. In 1983, Democratic Congressman Mo Udall of Arizona, who was famous for his wit and who had campaigned for president in 1976, was asked if he would run in the 1984 election. Udall responded, “If nominated, I shall run to Mexico. If elected, I shall fight extradition.”
 
Google Books
The Quote Verifier:
Who said what, where, and when
By Ralph Keyes
New York, NY: St. Martin’s Press
2006
Pg. 155:
If NOMINATED, I will not run. If elected, I will not serve.” Under pressure to run for president in 1871, William Tecumseh Sherman responded, “I hereby state, and mean all that I say, that I never have been and never will be a candidate for president; that if nominated by either party I should peremptorily decline; and even if unanimously elected I should decline to serve.” Thirteen years later, when Sherman-for-president fever revived, the general received a telegram from the Republican convention in Chicago telling him that, like it or not, he was about to be nominated. Sherman’s son Tom later recalled his father’s response to this telegram: “Without taking his caigar from his mouth, without changing his expression, while I stood there trembling by his side, my father wrote the answer, ‘I will not accept if nominated and will not serve if elected.’” This is as close as the historical record gets to the edited, more popular “shermanesque” statement of noncandidacy.
Verdict: Poeticized Sherman.
   
8 June 1871, St. Albans (VT) Daily Messenger, pg. 3:
Gen. Sherman.
NEW YORK, 8.
The following is published this morning. “Fort Sill, Commanch Reservation, May 27th, to the Editor of the Herald. I have been skirting the Texas frontier for the past month and here for the first time I meet files of Eastern papers, by which I see that quite an unnecessary fuss has been raised by a purported speech made by me at a supper of the Union League Club at New Orleans, the night preceeding my departure from tha city. Whoever reported that, as a speech by me committed a breach of propriety; for Gov. Warmouth, presided, and before I consented to respond to the call, I was assured by the President of the Society, that no reporters were present and that whatever was said, would be sacred and confined to the persons present. Now as to politics, I think that all my personal friends know my deep antipathy to the subject, yet as you seem not to understand me, I hereby state and mean all that I say, that I never have been and never will be a candidate for President, that if nominated by either party, I should peremptorily decline and even if unanimously elected I should decline to serve; if you can find language stronger to convey this meaning you are at liberty to use it.
 
I am your obedient servant,
H. T. SHERMAN, Gen’l.”
   
5 June 1884, Springfield (MA) Republican, pg. 5, col. 4:
GEN. SHERMAN’S ABSOLUTE “NO.”
The boom for Gen. Sherman is natural enough, but futile. Gen. Henderson sprang the suggestion on the convention somewhat prematurely in his opening speech, and the old general straightway sat upon the boom and crushed the life out of it by a peremptory letter, explicitly declaring that he would not accept the nomination if it were offered him, and if it should be pressed on him he would not serve if elected to the presidency. 
   
5 June 1884, New York (NY) Herald, pg. 3, col. 3:
Mr. Henderson was asked if he thought General Sherman would accept the nomination and replied that he did think so, but could more certainly ascertain by telegraphing the General. The hour at which the conference ended—nearly midnight—prevented getting an answer last night, but to-day ti came—a short, explicit and emphatic “No,” and declaring he would not accept the nomination or serve if he were elected.
 
5 June 1884, Chicago (IL) Daily Gazette, pg. 2, col. 3:
Before doing so they called in General J. B. Henderson and asked him to lay the matter before General Sherman. In reply General Sherman telegraphed that he would not accept if nominated and would not serve if elected.
   
Google Books
Memoirs of Gen. W.T. Sherman
Volume 2
By William T. Sherman
New York, NY: C.L. Webster
1892
Pg. 466:
The son of General Sherman tells the writer of these pages that he was sitting in his father’s office on June 5th, when a telegram came from General Henderson, still more urgeelected,” nt, demanding the right to use his name before the convention, and stating that he might be nominated at any moment by acclamation. his father telegrqphed immediately, “I will not acceot if nominated, and will not serve if elected,” etc.
 
30 March 1892, Monroe (WI) Evening Times, “Honor to Sherman,’ pg. 2, col. 3:
None of our heroes have been able to resist the fascinations and the dangers of the chief magistry, except General Sherman. His election would have been a certainty, and he knew it. But his answer was, “I will not accept if nominated, and I will not serve if elected.”
 
16 December 1908, Springfield (MA) Republicam, pg. 8:
SETH LOW’S POLITICAL CAREER.
[From the Brooklyn Eagle.]\it will be just an well to remember what Seth Low, after his last candidacy for mayor, said: “I have ended my career in municipal politics. Twice elected mayor of Brooklyn and three times a nominee for mayor of Greater New York, my five candidacies complete my career in municipal politics. If nominated, I will not accept. If elected, I will not serve.”
 
Google News Archives
29 November 1911, Boston (MA) Evening Transcript, pg. 19, col. 4:
A Denial That Denied
[From the New York Evening Post, Ind’t]
Everybody must sympathize with Mr. Roosevelt in the embarrassment and even pain, caused him by the repeated bringing forward of his name for the Presidency. Nothing that he does or says fails to be perversely misunderstood and twisted into an appearance of willingness to be a candidate next year. There can be no doubt of the Colonel’s overwhelming desire to keep his name off men’s lips and especially to prevent its being mentioned at the Republican Convention next year. This being so, it is a pity that some friend does not tell him exactly how to attain his purpose. Let him leave off his pained protests and profuse deprecation, and adopt from General Sherman the one precise and unmistakable formula for denying that he is a presidential candidate, “If nominated I will not accept, and if elected I will not serve.’
 
Google Books
January 1915, The American Magazine, pg. 89, col. 1:
“And that is definite!”
‘Definite?” said Fairborn smiling, for already he felt the happiness of a vast relief. “Yes; it is definite, and I wish you to make it definite; just as definite as—General Sherman, wasn’t it?—made his announcement when he said: ‘If nominated i will not accept, and if elected I will not serve.’ Do you understand?”