Final answer:
The next crisis Abraham Lincoln faced after South Carolina's secession was the problem of resupplying Fort Sumter, which ultimately led to the Confederate attack and the start of the Civil War.
Therefore, the correct answer is: option 'problem of Fort Sumter'.
Step-by-step explanation:
The given dilemma concerned whether Lincoln should attempt to resupply the fort, which remained under Union control but was surrounded by Confederate territory and on the brink of running out of provisions.
The situation at Fort Sumter was precarious, with Confederate forces in Charleston ready to interpret any attempt to resupply as an act of aggression, which could lead to open conflict and ignite the Civil War.
Lincoln was aware that supplying Fort Sumter would likely result in a Confederate attack, but he also sought to avoid initiating the conflict, thus placing the burden of starting the war on the Confederacy.
The tension escalated until Confederate forces commenced a bombardment of Fort Sumter on April 12, 1861, an event that marked the beginning of hostilities and the start of the Civil War.