I think Brazil offer much of the answer for how long slavery could survive. From my knowledge slavery was already in collapse prior to the abolishment, because a fall in the price of sugar, and the slaves was often left alone as their masters no longer had work for them, the slave prices had collapsed and the master no longer had the money to keep control over the slaves, which meant they began migrating away, which pretty much meant they became free.
So when do we see a similar crisis in USA, the answer would be the ball weevil in the 1920ties.
Brazil is not a good comparison for the slaveholding USA. To paraphrase one of my posts a few years ago about why slavery was much more entrenched in the southern US states than in Brazil:
a) the South had a much harsher view of race than Brazil did (or any other Latin American country or former French colony, come to that). The 'one drop rule' is the most visible manifestation of that, although far from the only one.
b) slavery was more profitable in the South than it was in Brazil, due to a combination of geography and better transport networks (although it still made considerable profits even in Brazil).
c) the South was in a federal republic, with separation of powers which made it much easier for a minority of slaveholders to block abolition even if the majority of southerners do come to want it. And which would apply either in slavery as part of the USA, or in an independent CSA.
d) Catholicism in Brazil had always emphasised the slaves were still Christians and that the Catholic Church retained responsibility for the eternal salvation of the slaves. This was a moderating influence. In the South, Christianity was used to justify slavery.
e) For a variety of reasons, fear of what would happen if slavery were abolished was much stronger in the South than in Brazil. Slave revolts were vanishingly rare in the South, but quite common in Brazil, yet the South was
more paranoid about them. Go figure.
f) In Brazil, the slave population decreased because deaths exceeded births. This meant that once the illegal slave trade was clamped down on by Britain, the slave population kept decreasing through natural attrition. In the South, the slave population grew by natural increase.
g) Brazil was much more vulnerable to British pressure than Southern states in the USA were likely to be. Britain had sent ships into Brazilian ports to attack slave trading ships. Britain never tried this with the Southern USA. Even an independent CSA would be more immune to such threats, if only because it did not rely on slave imports (Brazil did), and because slaves could be transported by land or inland waterways even if the British are patrolling the coast.
Even then, it's worth noting that slavery was abolished because Brazil had an Emperor who could abolish slavery by decree, and did so. And a fazendeiro-backed coup kicked him off his throne the following year as a result, although the coup backers didn't try to restore slavery, figuring that it would be too hard to turn back the clock.
Also, the timing of Brazilian abolition was in part an outcome of the ACW. The defeat of the CSA was a contributing factor to the proposals for gradual emancipation in Brazil in the 1870s, and it is unlikely that these would have started so soon without it.