This is a bit of a counter-factual question: as historians we can't really speculate on what would have happened if the US Civil War hadn't happened. Would slavery have ended? Would it have endured to the present day? It's hard to say anything definitive; human interactions tend to exhibit a kind of butterfly effect and the absence of a US Civil War introduces hundreds of thousands of variances the result of which, 150 years later, might be enormous.

But we can talk about what ended slavery in the rest of the Americas and why the US clung to the institution for as long as it did.

First off, understand that the US was not the last American holdout on the issue of slavery. While the British Empire effectively banned the slave trade in the early years of the 19th century, slavery continued in much of the world and the Western Hemisphere until nearly the beginning of the 20th, though it began its long slow slide towards abolition in the Americas roundabouts the American Revolution (abolition started to take off in the northern colonies at that time and the slave trade with Britain was officially suspended on account of the war).

Second, understand that the US had a better than average climate for an indigenous slave trade. Conditions in sugar plantations were unimaginably brutal and slavery in the Caribbean accepted that a constant influx of slaves was necessary to keep the plantations operating. Between the environment and the work conditions, the Caribbean did not have a self sustaining population of slaves. The American South, as brutal as it was, did not rise to this level and slavery there was able to persist even after the Atlantic trade had dwindled to smugglers and the Spanish efforts to keep the plantations in Cuba working.

Third, understand that many of the issues of the Civil War and the period that followed it are STILL unresolved. That's not just "the south will rise again" but long-standing philosophical differences in the role of government, human rights, equality, and racial/political identity still divide the United States along lines that parallel those bled over in the 1860s.

There is no good answer to your question, at least not within the confines of the study of History. We can ask ourselves, instead, what brought about the collapse of slavery in places which did not fight a civil war over the issue. I think, in that case, the best place to look is Brazil though, I confess, that falls far enough outside of my area of study that I would be remiss to speculate further on the topic. Someone more informed on the subject should take up the torch from here on out.