Given that the price of slaves and demand for them was growing, it seems your statement on it not lasting much longer is more wishful thinking than anything else. I mean, in 1861 they went to war to protect slavery and you think in 10 years or so they would have just voluntarily given it up? That makes absolutely no sense. We will never know how long it would have lasted, but clearly in the 1860's the south was clinging ever more tightly to defending slavery (to the extent they went to war to fight for it), so unless foreign military intervention forcibly changed US policy there was nothing that was going to abolish it short of a Constitutional Amendment. The only way to really view this issue is when we think a Constitutional Amendment reasonably could have been passed.
A Constitutional Amendment requires a 3/4ths vote of the states. Since we had 15 slave states in 1860, and if we assume they all vote against any such amendment, then it would have taken 45 free states, for a total of 60 states, to pass any such amendment. Since we currently only have 50, not looking good if the slave states did not voluntarily give up slavery. Now, if we assume that Maryland, Delaware and Kentucky eventually at some time in the 19th Century eventually become free states, that still means 12 votes against, which would require 36 votes for the amendment, which means a total of 48 states. The US admitted its 48th state in 1912.
If one more state, perhaps Missouri, became a free state, then that would leave 11 slave states, and thus needing 33 votes in favor, for a total of 44 states. The US admitted its 44th state in 1890.
Given the reality of the amendment process, I tend to think its unrealistic to think slavery gets abolished before 1890 and that assumes every formerly slave state votes against its former sister slave states, which is not guaranteed by any means. I think it probably lingers into the 20th century. This all assumes that history plays out like it did and I realize that games can be played with breaking up free territories into more than one state, and accelerating admission dates, so maybe we can move up the dates a little. It also assumes the admission of no more slave states, of course. But the above I think is a good framework for considering when slavery might have been abolished.that