Officially, the United States had banned the importation of slaves in 1807, with the Act Prohibiting Importation of Slaves. Slave smugglers still existed, mostly using the clipper ships, a new, extremely fast type of sailing ship that became very popular for transporting perishable cargoes in the 1830s and 1840s.

The domestic slave trade was much more extensive, however, as slaves in the United States generally had a much higher rate of survivability than in the British sugar islands. Thus, few if any slaves were ever imported from Jamaica and the other sugar colonies into the United States, as slaves in those territories did not tend to live long enough to reproduce, much less live to old age. In the US this was much less the case, though the existence of smuggling suggests that the expansion of the American use of slaves was at least sufficient to require more than could be acquired domestically. Increased British enforcement probably had some effect on American slave smuggling, but since this was a relatively small part of the overall American slave economy and was already illegal in the United States, I don't think it had a huge effect.

The bigger impact was likely cultural, as the US's 'mother country' and linguistic and cultural cousin exerted a great deal of influence here.