In case anyone actually cares to look in the legal issues behind the idea of the states "overriding" Biden to protect their borders, as opposed to just rabble rousing and threatening timely secession talk, I figured I'd offer a couple of interesting results from quick google search.
The first is Ken Cucinelli (remember him, the former " the Senior Official Performing the Duties of the Deputy Secretary of Homeland Security" from 2019 to 2021), which, to be honest, reads a lot like the writings of John C. Calhoun:
https://americarenewing.com/issues/policy-brief-how-states-can-secure-the-border/
The second is what appears to be a fairly bland, but decidedly non-Trumpist (its from 2004) view of the law regarding the Federal power to regulate emigration, including a few choice squibs on attempts from States to interfere with this implied power.
http://hrlibrary.umn.edu/immigrationlaw/chapter2.html
I'm not getting paid for this research or analysis, so I'm going to be lazy and not go much deeper, especially in response to a post like this one, but I'll offer this thought.
The federal power over immigration seems to be not much more express in the constitution than the right of privacy or any other non-expressly granted rights, like the endangered "rights of women over their own bodies" set forth in Roe. It would require some real legal gymnastics to overrule all the "precedent" talked about in the second link, but from an originalist perspective, its not really that much harder than what happened with Heller to reject all the prior decisions as dicta or inconsistent with the text of the Constitution, since there's precious little on the subject actually in the text aside from "naturalization" which is obviously distinguishable from immigration.
While I don't think OP actually thought much about or cared about the legal basis for, or even the implications of a full scale State rebellion by force against the Biden Administration on the issue of immigration, and tend to think he's just rabble rousing in advance of an uncomfortable spectacle by the Democrats about 1/6, its worth noting that this "Originalist" Supreme Court could fairly easily point out that that the Tenth Amendment reserves all powers not expressly granted to the Federal Government to the States or the People, and thus de-legitimatize any federal action against States that interfere with existing Federal border or immigration policy.
