To quote an old post of mine:
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Does this mean that there was no chance of Lincoln on the ticket in 1884? Not necessarily. For as Emerson has pointed out--and this is something I was previously unaware of--Lincoln did privately indicate that he would accept the vice presidential nomination under one circumstance: if Arthur were nominated for president. (Note that Lincoln was the *only* one of Garfield's cabinet that Arthur had retained.) Emerson writes (pp. 257-8):
"President Arthur was embarrassed and discouraged by the rejection of his party. After telegraphing his congratulations and support to Blaine, he ordered a carriage and disappeared from sight. History has shown, however, that the president did not seriously want the nomination. He did not 'bow out' of the contest, because to do so would raise suspicions about his health, cast doubt about his competence to handle the burdens of the presidency, and carry with it the implication of cowardice to both run on his record and to face possible defeat at the polls. But his health was the reason for his inactive candidacy. Although publicly unknown at the time, Arthur knew his Bright's disease was in an advanced stage and being aggravated by the stress of the presidency, and that if elected, he probably would not live out a second term.
"The knowledge of this fact makes it even more incredible to realize just how close Robert Lincoln actually came to being president. For, despite his disinterest in being the vice-presidential nominee, telegrams he wrote during the first day of the Republican National Convention show he was willing to accept the second place only if President Arthur were renominated. [It seems to me the correct word would be "nominated," since Arthur had never been nominated for *president.*--DT] Lincoln, believing his name might be presented to the convention for vice-presidential contention, entrusted longtime friend Norman Williams with a telegram to U.S. Senator Shelby M. Cullom from Illinois. In it, Lincoln instructed Cullom to withdraw his name from contention for vice president if it was presented. Confidentially, Robert instructed Williams to deliver the telegram to Cullom 'for his prompt action if any nomination for president is made by the Convention except President Arthur....If that nomination be made, telegraph me for further instructions, as my relations to him require me to consider my proper course.' The missive makes clear that if Arthur had been nominated for the presidency, and he asked Lincoln to join the ticket, Robert would have assented out of respect and loyalty to his chief. Since Arthur died in 1886. Vice President Lincoln would have become president.
"Had Robert's intentions been known inside the convention hall during the balloting, it is likely it could have swung sufficient votes to enable Arthur to win the nomination. Robert, however, took extra care that his telegram would not be revealed. Instead of sending it to the telegram station in the convention hall, he sent it to the Western Union main office and had Williams pick it up there, rather than have it delivered to him. And, if Arthur truly wanted to receive the nomination, he could have approached Lincoln previously and announced Honest Abe's son as his running mate should he be nominated. With Lincoln on the national ticket, the Republicans would have had a much greater chance of winning the nomination..."
Is Emerson right that if it had been known that Lincoln was willing to be Arthur's running mate, Arthur would have been nominated? I am not sure. At the first ballot of the convention, "Blaine received 344, Arthur 278, Edmunds 93, Logan 63, Sherman 30, with Joseph Roswell Hawley, Robert Todd Lincoln and William Tecumseh Sherman receiving parts of the remainder."
http://en.wikipedia.org/…/1884_Republican_National_Conventi… So it is certainly conceivable that if it were known that Lincoln would be his running mate, Arthur could have gotten more votes than Blaine on the first ballot. But this would still be less than a majority, and it is significant that 60 percent of Arthur's first-ballot support in OTL came from southern delegates.
http://books.google.com/books?id=PVwCtvcs3NgC&pg=PA215 (Daniel Klinghard, *The Nationalization of American Political Parties, 1880-1896*, p. 215). In other words, Arthur did poorly with delegates from Republican areas, and did best with patronage-dependent delegates from an area of the country that the Republicans had no chance of carrying. Having Lincoln as a running mate would strengthen Arthur with northern delegates, but I am not certain that it would strengthen him enough. As noted, he had plenty of enemies in the party (though of course this was also true of Blaine).
https://www.alternatehistory.com/fo...coln-possibly-president.350654/#post-10604233