I would say that some of the most challenging elements that Lincoln faced was maneuvering the Union into a position to win a long term conflict. It is easy to overlook the fact that few saw the Civil War developing into the trajectory it did. There was a strong belief that the South had some intrinsic advantages such as defense of their home territory and not needing to invade the North, as well as superior military leadership. The advantages of the North such as a population increase as well as factory production and the blockade were made for the long term and would not provide decisive change to the war's outcome in the short term. Lincoln recognized early on that there had to be a long term approach needed in the war, so moving towards that end was a fundamental challenge. This pivot included the seemingly endless parade of generals that Lincoln went through reflected such a difficulty. From McDowell's lack of victory at Bull Run to McClellan's cautiousness and conservative approach, Lincoln's primary difficulty at the start of the war was both embracing a long term strategy to win the war and finding the personnel that would be able to accomplish such an end.
his main problem was the south secceding from the united states.