William C Davis’ history of the Confederacy, Look Away, points out there were four main political camps - Nationalist (favoring a stronger central government), Moderates (generally opposed to the power of the Davis government), Fire Eaters, and Reconstructionists. The Reconstructionists lack political figures to rally behind. Leaders of the other three factions are deeply divided, sometimes over the issues, but just as often over personal animosities.
Since they’re all nominally Democrats, I see a couple likely possibilities for the election of 1867. They hold a party convention where no candidate receives a majority and the Democrats fracture into separate Nationalist, Moderate, and Fire Eater Parties. Less likely, one faction wins out and gets to keep the Democrat name, the other two spilt and form their own parties. Either way it’s a three way contest that will probably need to be decided by the Confederate House of Representatives, if it can. Alternatively, candidates might publicly nominate themselves, short-circuiting the whole party convention process. This would lead to a minimum of three candidates, there could easily be half-a dozen or more, and the House gets to decide between the top three candidates – if it can.
The Confederacy was founded with the idea that any state could leave at any time for any reason- like your candidate not getting elected. There’s a good chance the Confederacy will lose some states over the 1867 election. It could even disintegrate. At which point the lucky winner faces the problem that any significant decision that he makes also risks the Confederacy losing states or fragmenting.