Andrew Jackson was faced with a similar dilemma during his presidency when South Carolina threatened to secede over the Tariff of Abominations (colloquial name). He used a carrot and stick method: slightly reduced the tariff while at the same time passing a "Force Bill" that would have authorized federal troops going in to South Carolina if they seceded. The rest of the South saw that Jackson wasn't someone to be trifled with, and support for South Carolina's cause diminished. Keep in mind this is only about 20 years before the Civil War.

So in short, Buchanon is criticized for lame-ducking during one of the most crucial moments in American history. Since the Southern states could rely on him to do nothing, secession was now much more feasible to the South than it was under a stronger president like Jackson.