The general assumption of the Founders was that slavery was so much weaker as an economic system compared to free-labor capitalism (although that term hadn't come into usage yet) that it would soon fade away. "Soon" certainly had a different meaning for the slaves themselves than for their owners. But the abolition of slavery in the Northern states seemed to support that assumption. It had also been generally assumed that when the US banned international slave trading that the relative number of slaves would decline over time.
The historian William Freehling has given really helpful accounts of that process in his two-volume Road to Disunion work.
The relative inefficiency of the slave economy displayed itself over the decades even despite the cotton gin. But that technological innovation made a difference, as Nabors explained:
The Republicans [in their accounts of slavery] pointed to this period [the early Republic] as that during which the slave states were undergoing fundamental change, that is, when the power and ambitions of oligarchy were quietly gestating. The most important event that accelerated this change was a historical accident. Eli Whitney’s invention of the cotton gin at the end of the eighteenth century allowed cotton cultivation over greater parts of the slaveholding states and created the demand for more slaves.And he cites this observation, "In a public speech to his constituents, Representative Henry Deming of Connecticut declared, 'The invention of Whitney adjusted the social position and relations of our Southern brethren, more decisively, than their cotton-perfecting soil and climate'.”
The PBS webpage for Africans in America (KQED; n/d) notes:
Although there was some hope immediately after the Revolution that the ideals of independence and equality would extend to the black American population, this hope died with the invention of the cotton gin in 1793. With the gin (short for engine), raw cotton could be quickly cleaned; Suddenly cotton became a profitable crop, transforming the southern economy and changing the dynamics of slavery. The first federal census of 1790 counted 697,897 slaves; by 1810, there were 1.2 million slaves, a 70 percent increase.Anthony Kaye gives a broader look at the invention of the cotton gin and points to another type of innovation that also contributed significantly to the increased productivity of the slave economy (The Second Slavery: Modernity in the Nineteenth-Century South and the Atlantic World Journal of Southern History 75:3, Aug 2009):
Angela Lakwete has debunked the myth that the cotton gin was Eli Whitney's invention. He was one of many mechanics around Augusta, Georgia, experimenting on roller gins to increase output. Manufacturers complained his wire-toothed gin tore and tangled the fiber and impeded textile production down the line. The saw gin that he is remembered for was actually another mechanic's handiwork and appropriated to Whitney in court. Only after a long transition lasting until 1830 did the saw gin become ubiquitous. The cotton gin was thus the work of many hands-mechanics, free and enslaved, who modified and made gins with rollers and saws; forward-looking planters and skilled slaves who adopted the saw gin; all in all, "an industrializing, modernizing, and slave labor-based South."But technology couldn't save the Slave Power from the effects of its incompatibility with democracy.
A skein of biological innovations, long obscured by historians' traditional focus on machinery, was also critical to the expansion of slavery. While machines enabled planters to put more land into cultivation and work more slaves, manipulating the natural properties of cotton and sugar increased the crops that slaves produced per acre. With little knowledge of genetics, a rudimentary understanding of plant breeding, and dogged empiricism, agriculturalists in Mississippi, Tennessee, and Georgia molded short-staple cottons for varied environments from the interior of the seaboard states to the lower Mississippi River Valley.