That's Davis's story, but we have to ask whether it is true:
"Shortly before he accepted the presidential nomination of the Richmond convention, Breckinridge met with Jefferson Davis and Robert Toombs. In his memoirs, Davis states that the subject of the meeting was to persuade Breckinridge to accept the nomination, so that Davis might have the leverage to convince both Bell and Douglas to leave the race in favor of a compromise candidate who could save the Union (Davis, 1890: p. 52). According to Davis, Breckinridge and later Bell supported the ‘‘fusion’’ idea and agreed to withdraw, but Douglas obstinately refused to leave the racedthus, the fusion plan failed. Nevertheless, Davis’s biographers speak in grand terms about his efforts to avoid secession and the coming war through his meetings with Breckinridge, Bell, and Douglas. For example, William C. Davis (1991: p. 282) states that 'in one of the most statesmanlike efforts of his career, [Davis] tried to avert calamity by taking the same sort of managerial hand in affairs that he exercised in the Missouri Compromise repeal.'
"Is this story true? Though most historians accept these events as fact, the primary evidence for much of this is sparse. Aside from Davis’s own memoirs--written in 1881, two decades after th efact--there is *no* evidence that (a) Bell agreed to leave the race, (b) Davis met with Douglas, or (c) Douglas refused to leave the race. In fact, there are no known letters or other documents that suggest that Bell ever considered leaving the race; yet, there is primary evidence that Douglas was willing to leave the race (see Crenshaw, 1969; Wells, 1971; Johannsen, 1961, 1965). Though Davis’s version of events is now widely accepted, there is good reason to believe that his memory might have been something less than perfect. Given that Douglas (d. 1861), Bell (d. 1869), and Breckinridge (d. 1875) all had died long before Davis released his memoirs, and therefore could not contradict (or substantiate) his claims, Davis may have concocted the fusion scenario in an attempt to rehabilitate his reputation."
http://faculty.virginia.edu/jajenkins/ES.pdf
For similar skepticism, see Damon Wells, *Stephen Douglas: The Last Years 1857-1861*: "Davis's account is strangely lacking in details. He never tells us if his proposals were submitted in writing, or if a conference actually took place between the three candidates. There is no record to suggest that Douglas either met or corresponded with Davis at any time in the summer of 1860. The Little Giant mentioned a proposal to withdraw from the race only twice during the entire campaign and in doing so made no mention of Davis. Douglas and his followers would have distrusted any such scheme. The Jefferson Davis of 1860 was not the Davis of 1861 who led a South with some pretensions to unity. There was no guarantee that he could make good on his promise to withdraw Breckinridge and Bell from the race. Douglas further reasoned that if he withdrew, no Democrat could be elected, but if Breckinridge pulled out, Douglas still might win. Even should Douglas lose, he would still be in firm control of the Democratic party. Finally, the most likely compromise candidate would be Horatio Seymour of New York, whom Douglas had gone to great lengths to block at Baltimore."
http://books.google.com/books?id=7BmCBAAAQBAJ&pg=PT245
Assuming Davis's account is true, who might a compromise candidate have been? As noted, the name that is usually mentioned is Horatio Seymour, former (and future) governor of New York. Of course, Seymour could get every vote that Douglas, Bell, and Breckinridge combined got in California, Oregon, and New Jersey (the only states where Lincoln got any electoral votes without getting an actual majority of the vote) and Lincoln would still win.
http://psephos.adam-carr.net/countries/u/usa/pres/1860.txt The only question is whether Seymour's home-state advantage--combined with the possibility that some voters would rather vote for an individual than for a fusion slate of electors--would enable him to carry New York. I doubt it. The Douglas/Bell/Breckinridge fusion ticket in New York got only 46.3 percent of the vote. Seymour might do better than that, but I doubt he could make it to 50 percent.