Back in 1790, nobody wanted to restrict all migration. Very few people even wanted to restrict any migration. (Which doesn't mean they wanted open borders completely, but that they didn't want to exclude any groups a priori.) That kind of sentiment arose later. And even then, I have my doubts. Some kind of (alt-)nativist movement could sweep into power, but i don't see it staying in power.
If you want to end all or almost all immigration as of 1790 or thereabouts, you need a POD that goes further back. A POD that will inevitably change the nature of the USA, to the point where you're looking at a completely different revolution. I recall a thread where someone posed the challenge of having the Americas go completely isolationist. I suggested a religious POD, where pre-independence North america gets swept up in some sort of new Christian movement that sees America as a special, "pure" country that must shield itself from the sinful outer world. If you just want the USA affected, then that idea becomes far more realistic than if (as in that thread) you want it to sweep up all the New World.
So, let's see: the first great awakening (1739s-1740s) produces such a new cult/denomination. As tensions between colonies and Britain arise, this new denomination becomes closely tied to the cause of independence. An alt-ARW sees the alt-USA go independent. Ideally, the alt-USA would (thanks to the religion having spead there) include Upper Canada, New Brunswick, Nova Scotia and St. John's Island (now Prince Edward Island). Why? So that the alt-USA borders Francophone Quebec, whick is full of scary Catholics, which makes immigration from those parts far less likely. Alt-USA closes itself off to all immigration, goes full isolationist, and becomes a Tokugawa-style quasi-theocracy.
How this religion views slavery decides what happens in the South. If the religion is opposed to slavery, then you may expect the South to stay out of the alt-ARW altogether, starying with Britain. If the religion embraces slavery, I can vaguely see the slavocrats accepting that no more slaves will be coming (due to the closed borders), in return for certain political concessions. However... since the South made quite a profit from exporting raw goods, I suspect that a POD such as this is likely to lead to an alt-USA that simply doesn't include the slave states.
A religious POD is pretty much the only thing I can imagine that's powerful enough to make this kind of isolationism happen. So ultimately, the very idea will demand that we end up with an alt-USA that isn't really recognisable to OTL. It's a sort of funhouse mirror version of the North-Eastern USA, that accentuates its historical association with dissenting religious factions, a strong puritanical streak, and a tendency towards 'utopian' religious colonies.