It is conceivable that the pro-southern wing of the Democratic Party might nominate Davis rather than Breckinridge. And *if* the race goes into the House, whoever the southern Democrats nominate could theoretically win if he gets enough southern Americans/Oppositionists/Constitutional Unionists/Whigs to vote for him. But in the first place, the race did not get as close to being thrown into the House as some people think. It is true that if Lincoln had lost California, Illinois, Indiana, Oregon, and the electoral votes he won in New Jersey, he would only have gotten 145 electoral votes--seven less than needed to win. The problem, though, is that Indiana wasn't really that close; Lincoln won it by 8.7 points. Likewise, if the "fusion" anti-Lincoln ticket in New York would have been able to carry that state, the race would go into the House; but it didn't really come that close, losing the state by 7.4 points.
https://en.wikipedia.org/wiki/United_States_presidential_election,_1860 (Nor do I think that Seward would have lost IN or NY; he might have lost very narrow Lincoln states, but that would not be enough to deprive him of an Electoral College majority.) And in the second place, it is unlikely the southern Democrats will nominate Davis; Breckenridge is a better choice because he is from a state (KY) that often voted Whig and where Bell will be a strong candidate (whereas MS is safely southern-Democratic), and also because while 'sound" on slavery, he is not considered a fire-eater and had even backed Douglas for re-election in 1858 despite his disagreements with Douglas over the Freeport Doctrine.