Early Republic
The first potential fracture is the War of 1812; New England animosity wound up culminating in the Hartford Convention and while New England obviously did not secede these are the rumblings of dissatisfaction (prior to the war the Jefferson Embargo Acts were not popular). I really don't see that resulting in a Civil War, I am envisioning a simple unraveling of the early Republic.
The second potential point was the Nullification Crisis. Nobody joined South Carolina though.
After that point, I really think the next potential fracture point is the beginning of the Mexican War itself, and once the US choked on that massive slavery question we had a ticking time bomb. I see that going off as early as 1850 with California admission as a free state or with Congress' blocking of Kansas' admission as a slave state under the Lecompton Constitution (Kansas would be admitted in 1861 post-South Carolina's secession)