There are a lot of factors that contributed to the South's secession which might not apply ten years later.
1)James Buchanan was clearly inept and unable and unwilling to protect Federal installations from the secessionists. A President more willing to use force and authority would deter a lot of fence sitters.
2) The secessionists were very well organized in 1860-61, but the unionists were not. This was a result of the earlier secession crises. The secessionists retained their organization and actively planned for their next attempt; while the Southern unionists failed to organize beforehand. Would this dynamic still exist ten years later?
3) If for various reasons (and many have already been documented) there were large parts of the South which would be unlikely to secede, would the other states risk going it alone? There was a belief in 1860 that the slave states would all eventually secede. If by 1870-1872, it appeared that not just the Border States, but even some of the Upper South, would absolutely refuse to secede, then it would give the Deep South a great incentive to not rebel.
South Carolina was always the fire eaters's capital, and it's possible that state will still secede. However, there is no guarantee even the other Deep South states will follow them.
A secession crisis in the 1870s could very well be contained and limited to only South Carolina, or just the Deep South. Most likely, the crisis - even if it comes to war - is over in two years.