A nation-state would be able to levy federal taxes. There is no reason why a new Confederacy would not be able to levy the equivalent of income and SS/medicare taxes and continue these payments. It should even be able to honor federal pensions. It should be able to do this more efficiently than the federal government does today. One big advantage of the prospective Confederate states is a higher worker/retiree ratio.
And these states collectively are not lightly populated. A new Confederacy could easily encompass better than 100million people. And they would get to tax businesses operating in their territory that are headquartered in New York or California or anywhere else, just like France taxes Microsoft.