This may come down to a few states challenging the federal usurpation of state power to approve or deny immigration of foreign nationals. That usurpation was accomplished piecemeal, with a provision concerning citizenship in the first section of the 14th amendment and then later by legislation. There was never a Constitutional amendment passed to grant the federal government the power to admit immigraqnts and grant them citizenship. That was a reserved state power and under the terms of the 10th amendment, it's still a reserved state power which can be exercised by any or all of the states.
To silence the critics of ethnic profiling by the states, the 14th amendment would have to be repealed. I think it should be anyway, but this situation is a very strong contemporary argument for doing so. Ashcroft announced that ending racial profiling would be a priority in his administration of the DoJ. I don't think he has any political courage in this area myself.
We may not agree on methods for implementing the solution, but we agree on what the solution obviously is. To me it's very obvious.