The problems with delaying the cotton gin are twofold:
(i) it isn't plausible for it to be delayed by more than a handful of years (10 at most); and
(ii) paradoxically, delaying the cotton gin may strengthen the geographical spread of slavery within the USA.
For the first, the cotton gin was a simple enough invention, with hand-controlled equivalents already present in other parts of the world. The British demand for cotton was also high enough that lots of people were throwing lots of money at potential solutions. Someone would have come up with a similar version pretty quickly. I think that a more than ten-year delay is implausible.
For the second, the invention of the cotton gin had the effect of concentrating slave populations in cotton states. This led to the involuntary migration of large numbers of slaves south and west from the border states and Upper South into the cotton states, following the invention of the cotton gin. One of the side-effects of this was that it stopped to free states being turned into slave states.
Illinois and Indiana nearly turned back into slave states in OTL in the 1820s as it was. Although nominally illegal, slavery was commonplace in the downstate areas of those states in the 1810s and 1820s, due to slaveholding Southerners moving there from Kentucky, Virginia etc. After the spread of the cotton gin, slaves and slaveowners were drawn further south instead, and while there were various pushes to legalise slavery after statehood, it never eventuated. If the cotton gin is delayed, more slaveowners move into those states in the 1810s and early 1820s, leading to greater internal pressure to legalise slavery - and Congress has no authority to stop them once they are states.