He's not very J whatsoever, and did the very INTP-ish thing of agonizing over what decisions he was forced to make, according to the two bios I've read. He also had a lot of trouble determining what level of involvement he would make in running the war, wanting to hand over power to his generals but being very unhappy when his generals did things that he thought did not make sense and/or violated how he thought the war should be approached. (he so obviously wanted to leap in and just issue commands, then would rein himself in, and back and forth... just make a decision!)
This was easily the best bio I've seen:
http://www.amazon.com/Lincoln-David-Herbert-Donald/dp/068482535X
I consider the Gettysburg Address to be one of the most beautifully concise speeches I've ever read -- capturing the content of the situation into the shortest amount of words possible, so much so that many people missed the speech. People didn't appreciate it (as is typical) until after the fact, when the intellects started to examine it more closely. It's an equation capturing the essence of how the battle (and the war) should be viewed... almost a philosophical proof.
If INTP is right, he was more the "social/easy-going" sort than the reclusive/avoidant sort. IOW, he had decent people skillz. He was kind, witty, a bit gangly/awkward, down-to-earth, laid-back, non-presumptuous, felt deeply under his rationality, married an ESFJ (stabilizing her as much as possible)...
... he felt that slavery was wrong but at first was far more concerned about secession and preserving the union... only later seeing that slavery was an intertwined issue that he had the opportunity to deal with and was in fact needing to be dealt with as the war progressed, and there was no longer a reason to avoid it. He constantly adjusted to situations as they unfolded.
His cabinet was NOT stocked with "yes" men at all. In fact, he created more issues for himself because he placed people who disliked him and even considered him an enemy, because he valued the reality that they would give him other opinions, and his goal seemed to be to put all the ideas together, let them fight it out, and then give credence to the ideas that survived. He was very rigorous, mentally; but seemed very naive of the politics that could derail his rather idealistic way of approaching a "thinktank." (He just didn't seem to realize how petty and personal people could be in situations where he would naturally detach and act in a fair and balanced manner.) He also had a spirit off melancholy about him, and winsomeness. And he had that sense of impending events... the INTP-ish grasp of cause-and-effect and where a situation was likely to go if the system worked as expected... even potentially resulting potential premonitions of his own death.
... oh, the list goes on and on.
As an INTP, he would be an amazing success story. He only won the presidency originally because he was the most palatable of all the candidates to both sides (he was placed in power by political jockeying between both parties). THere was a time during the war he seemed likely to lose re-election. It was only as the war was ending and after the war had ended and he had been killed, that people really started to realize what a good man and human being he actually was, and how many other types of leaders would have not responded as well to the events of that time. (They would have either tried to lock things down, resulting in a later worse explosion; or been completely overrun by them; but Lincoln kind of "rode the surge" with stamina, flexibility, and long-term vision.)
I would definitely not label him a "conventional politician" by today's standards, but a good man who did the best he could in a very difficult situation that would have destroyed less-flexible and less-perceptive/thoughtful men, who just happened to be a political leader at the time. (Talk about providence.)