Throughout the 1840’s and 1850’s, many white Americans genuinely believed that slavery would eventually (and inevitably) die. Even Abraham Lincoln, the man who signed the institution’s death warrant, firmly believe throughout his career that slavery would ultimately die if it was just prevented from expanding.
Now, to me, this seems more like a convenient lie repeated rather than an actual truth. Given the abject horror of the institution, I imagine that the belief it would one day go away naturally would be helpful for the “anti-slavery but not abolitionist” type white Americans.
But was there any evidence that it would end? Were there any “signs of slavery dying” that people noticed, such as it becoming less profitable, or more enslaved people were becoming free? Even if such data was false or misleading, was there anything Americans would have used to back up the assertion that “slavery will inevitably die off”?
The idea that slavery would eventually "die out," without any external intervention, enjoyed some currency among Colonial America and the Young Republic's slaveholding elite in the 18th century. At that point, leading thinkers would have told you that slavery was a "necesarry evil," what it was necesarry for varied depending on whom you asked, that would, with time, die out on its own.
Indeed, in the years immediately following the Revolutionary War, the plantation South was in shambles. Thousands of enslaved workers had escaped during the way, seeking freedom, British and American forces had burned plenty of plantations. Not only that, but a new political language influenced by ideas of natural rights, and slavery as the ultimate political evil, enjoyed new currency among America's elites, North and South. Popular evangelical faiths like Baptism condemned slavery even as they found enthusiastic converts among the slaveholding elite. In places like Virginia, some legislators made abortive efforts to begin a process of gradual emancipation that they hoped would lead to slavery's slow, peaceful death over a few decades or generations.
But it was not to be. Though legislatures in the Northern states, one after the other, successfulyl enacted gradual emancipation programs (though its worth noting that some, like New Jersey's, were so protracted that there were small numbers of enslaved people in Northern "free" states in 1861!), the Southern states had traditionally depended upon slave labor for their economic prosperity, and their elites were always themselves large slaveholders. Instead of a gradual diminution in the South, slavery was revitalized and intensified, with the pace of slave ship imports of captive laborers going up greatly in the closing decades of the 18th century (before the United States ceased officially participating in the transatlantic slave trade in 1808).
The invention of the cotton gin (making cotton a textile that oculd be produced in large volumes), Indian Removal opening up millions of acres of the world's most fertile soil (in the Mississippi River Valley and the "black belt" regions) to white settlement, and the United States conquering inexorably Westward meant that, by the 1830s, American slavery was on a steady course of dramatic expansion. In 1821, the United States produced 354,000 bales of cotton, almost all of it grown and harvested by enslaved workers on plantations. In 1859, the United States produced more then 4 million bales.
In the 1850s, the United States practiced slavery on a larger and more profitable scale than it ever had before. And slaveholders had become radicalized by the proslavery ideology that developed in the United States in the 1830s. Forming a lockstep defense of their way of life in the face of a world that increasingly saw slavery as a political liability and moral evil, proslavery thinkers rejected the idea that slavery was a necesarry evil, and that ending it would be desirable. Instead, they insisted, slavery was the most benevolent and just system of labor relations that humanity could acheive, and it ought ot be preserved in perpetuity. Some of the really fanatical proslavery thinkers, like George Fitzhugh, even argued that slavery was so good for so many people that almost everyone one arth should be enslaved, regardless of skin color. By the 1850s, many proslavery thinkers felt they had been vindicated by the disastrous economic consequences of British emancipation in the Caribbean (it turns out that, when given a choice, most people don't want to grow sugar cane, so the British began importing indentured "coolie" laborers from places like India to work the plantations instead as profits cratered), and that slavery would be the backbone of the modern world.
Some Northerners in this period hoped that market forces would destroy slavery. After all, thinkers like Frederick Law Olmsted wrote, how could a society that made its profits through violence and terror compete with a free labor industrial capitalist society, where people work in the hopes of bettering their lives? These sorts of arguments often ignored both how profitable slavery remained (in 1860, the richest state per capita was Mississippi), and the problems of exploitation in their own "free labor" system. Their evidence was that the North, in their eyes, was modern and enjoyed modern technology and living standards, while slavery had made the South impoverished and backward. When Olmsted visited the Slaveholding South, he expressed contempt for the "backward" tools and techniques employed by white Yoemen farmers (who were not slaveholders) and their minimal involvement in the larger national market, seeing a further vindication of the North's way of doing things. Surely any rational person would choose the more dynamic economic model that offered more opportunities for everyone, and surely market forces would eventually force them to make that choice!
But thinkers like that generally did not believe slavery was dying out, only that it should and would die out eventually. In the 1850s, Southern defenses of slavery became ever more radical and intransigent, with slaveholders refusing to accept any limits on the institution or its future expansion as they became ever more terrified that such limits would be imposed on them imminently by radical Northern antislavery forces. Ultimately "slavery is dying out naturally" was just not an argument you would have often heard on the eve of the Civil War.