I had a post on this a few years ago (as usual, apologies for links that may no longer be working):
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Woodrow Wilson for President--in 1924?!
Yes, Woodrow Wilson died on February 3, 1924. But in 1923 the idea of his seeking a political comeback did not seem absurd. As John Milton Cooper, Jr. writes in *Woodrow Wilson: A Biography* (New York: Alfred A. Knopf 2009), pp. 588-9, 1923 was
"...the best time in his life since the [1919] stroke. Nearly everyone who saw him commented on how much better he looked. In June, a senior reporter for *The New York Times,* Richard Oulahan, wrote a long story about him. Oulahan noted that he still limped but did not drag his left foot, and he used a cane but could stand without it and get in and out of a car without help. 'He has good color, his eyes are clear, his voice is strong, his cheeks are filled out, and he has lost that emaciated appearance of face and body which shocked those who saw him on his first outing after his long siege of confinement to the White House.' The reporter noted that from all reports, mentally he was 'the Woodrow Wilson of the stirring days of September, 1919.' He compensated for lack of paid work with attention to public affairs. Oulahan dismissed rumors that Wilson was personally interested in the race for the Democratic nomination in 1924, and he noted that Wilson had not committed himself to any of the contenders, not even his son-in-law McAdoo. This newspaper story read a lot like the one by Louis Seibold in *The World* three years earlier, which had set the stage for the abortive stab at a third-term bid..."
http://books.google.com/books?id=lxoOdaCDbpEC&pg=PA589
Twice in November, 1923, Wilson spoke out publicly on current events. On the day before the fifth anniversary of the Armistice, he gave his first and only talk on the radio. Much of it was devoted to scolding his fellow Americans for failing to live up to their obligation to maintain peace and for withdrawing into "a sullen and selfish isolation"; yet he expressed confidence that the nation would "retrieve that fatal error and assume once more the role of courage, self-respect and helpfulness which every true American must wish to regard as our natural part in the affairs of the world."
http://www.nps.gov/nr/twhp/wwwlps/lessons/14wilson/14facts3.htm As Cooper notes, pp. 591-2 "Stations across the country carried the talk, and some towns set up loudspeakers in auditoriums, allowing thousands of people to hear the ex-president's voice for the first time. It might have served as a kickoff for a campaign." The next day, Wilson addressed an estimated 20,000 people who had gathered in front of his S Street home to pay him an Armistice Day homage, assuring them "I am not one of those that have the least anxiety about the triumph of the principles I have stood for. I have seen fools resist Providence before, and I have seen their destruction, as will come upon these again, utter destruction and contempt. That we shall prevail is as sure as that God reigns."
(In the radio address, Wilson had criticized France and Italy for having made "waste paper of the Treaty of Versailles." In January 1924, Wilson went even further in discussions with Raymond Fosdick who had stopped by for a visit: "Some day another Bismarck will arise and the Germans will wipe the French off the face of the earth--and I hope they do." Cooper, p. 593. I knew that Americans by 1923-4 were pretty disillusioned with Our Oldest Ally, and that many people tended to sympathize with our recent German enemy on things like the occupation of the Ruhr. But I never heard any other American take it quite *that* far. Wilson also told Fosdick that "Mussolini is a coward. Somebody should call his bluff. Dictators are all cowards.")
Besides speaking, Wilson was also writing. His *Atlantic* article "The Road Away from Revolution" argued that while it could reasonably be asserted that "the abstract thing, the system, which we call capitalism, is indispensable to the industrial support and development of modern civilization" yet the attack on the system, of which the Russian Revolution was the most obvious example, did have its legitimate points: "Have capitalists generally used their power for the benefit of the countries in which their capital is employed and for the benefit of their fellow men? Is it not, on the contrary, too true that capitalists have often seemed to regard the men whom they used as mere instruments of profit, whose physical and mental powers it was legitimate to exploit with as slight cost to themselves as possible, either of money or sympathy?"
http://gutenberg.net.au/ebooks03/0300991.txt Wilson's only answer to the problem of revolution was to urge the Christianizing of economic and social life. The article was attacked then and later for its vagueness as to just what this would entail and how it could be brought about. (Wilson's brother-in-law Stockton Axson told Wilson to resist the suggestions that the article be expanded and elaborated. If anything, Axson said, the article should shortened: "This is not an argument, it is a challenge." Wilson agreed to Axson's suggested cuts. Cooper, p. 584.)
Wilson was not satisfied with any of the potential 1924 candidates for the Democratic presidential nomination, including his son-in-law McAdoo. Except for Newton Baker, none of them seemed really committed to the League, and Wilson though he liked Baker said he "ought not to run in 1924. He ought to be saved for 1928." McAdoo had made the big mistake of doing legal work for some oilmen later to be implicated in Teapot Dome. [1] Unlike McAdoo, Wilson had never been a prohibitionist (he had vetoed the Volstead Act, though largely on technical grounds--a veto which Cogress promptly overrode) and indeed he did not really care much about the ethnocultural issues that were tearing the Democratic Party apart, especially Prohibition and the Klan. (Incidentally, as I note at
https://groups.google.com/forum/#!msg/soc.history.what-if/ozMalZPiiJs/IGPblZ6mX7AJ it may well be a myth that in 1915 he praised "Birth of a Nation" as being "like writing history with lightning." Three years later, he told Joseph Tumulty that the movie was "a very unfortunate production" and he wished it would not be shown "in communities where there are so many colored people." Cooper, p. 273. As Cooper notes, this was a matter of deploring the stirring up of emotions, rather than objecting to the underlying racist message of "Birth of a Nation." Still, it might come as a surprise to people who think of Wilson as practically a Klansman himself. [2]) As for the anti-evolution crusade of Bryan (who was occasionally mentioned as being a possible nominee yet again in case of a deadlocked convention) Wilson said "of course like every other man of intelligence and education, I do believe in organic evolution. It surprises me that at this late date such questions should be raised."
http://en.wikiquote.org/wiki/Woodrow_Wilson
Wilson's preferred candidate for 1924 was himself; he even wrote fragmentary notes for an acceptance speech and a third inaugural address. They showed that he still believed in a combination of internationalism abroad and progressive reform at home. 1924 was probably not the year for such policies to prevail, either in the nation as a whole or even within the Democratic Party. And yet, let us say that Wilson's relative good health of 1923 had lasted for another year or two. Cooper suggests (p. 594) that "with radio at his disposal, even as a semi-invalid he might have made a better compromise candidate than the one the party finally picked--the obscure and lackluster John W. Davis."
(If nominated, Wilson would no doubt be disappointed by the Democratic platform because instead of pledging US membership in the League, it merely promised a referendum on the issue.
http://www.presidency.ucsb.edu/ws/index.php?pid=29593 Yet Wilson might still be willing to run on such a platform, because he was capable of convincing himself not only that he could win but also that the League could prevail in such a referendum--and the second hope was neither more nor less delusional than the first. What might disturb him more would be the platform's reference to "such reservations or amendments to the covenant of the league as the president and the senate of the United States may agree upon.")
So the nomination of a semi-healthy Wilson by a deadlocked Democratic convention was not out of the question. But that he would defeat Coolidge in November was extremely implausible--though he might, for example, get the support of some trade unionists and western progressives who voted for La Follette rather than the conservative Davis in OTL. (He would get virtually no African American votes, of course, but neither did Davis.)
To actually have Wilson elected in 1924 requires not only that Wilson remain at least as healthy as he was in 1923 in OTL, but also that a lot of even less likely things happen--e.g., Harding lives, manages to escape the taint of the scandals just enough to win the nomination, and then is devastated by new revelations before the election...
(There would of course be the third-term issue, yet it could be argued that the point of the no-third-term tradition was to prevent an incumbent president from using the powers of his office to perpetuate himself indefinitely in the White House, and that the tradition should therefore be interpreted only to prevent a third *consecutive* term. This was the argument used by supporters of Grant in 1880 and of TR in 1912. Yes, both of them lost, but it is not clear to what extent the no-third-term tradition was responsible for their failures to win the GOP nomination. In the case of Grant, there were memories of the scandals of his administration; in the case of TR, there was the difficulty of preventing the renomination of an incumbent president.)
[1] By contrast, when Wilson and his former Secretary of State Bainbridge Colby were law partners in 1921-2, Wilson was very scrupulous about what clients the firm should take. He declined to involve himself in a case about the Costa Rica-Panama boundary and in another one involving Ecuador and some American banks. He did agree to represent the Western Ukrainian National Republic's bid for recognition by the League of Nations. (Although, as Colby soon concluded, there was not much they could do for the Western Ukrainians; Poland was intent on treating their territory as an integral part of Poland.) Most important, in August 1922 when representatives of the oil company owned by Harry Sinclair asked the firm to represent them in the upcoming Senate investigation into the Teapot Dome leases, and when they offered a huge retainer, Wilson smelled a rat: "Colby must be a child not to see through such a scheme," he told his wife Edith. (Cooper, p. 581)
[2] So might a couple of 1922 items mentioned in a 1923 *Time* listing of Wilson's 1921-3 activities:
"Thanks State Attorney Lyon, of Virginia, for saving Negro from mob. July 30"
"Spurns charge of church favoritism made by Klan official. Aug. 25."
http://content.time.com/time/magazine/article/0,9171,716262,00.html (only available for subscribers)
https://www.alternatehistory.com/forum/threads/woodrow-wilson-for-president-in-1924.338499/