The reverse would be in essence a confederacy. That was exactly the conflict at the time—federation vs. confederacy. But the supremacy of federal government only exists (or should only exist) within the express powers granted by the Constitution. The so-called elastic clause that is too often misused is not a blank check. The Constitution specifically says that additional powers can exists only for enforcing the express powers. That’s where we’ve gone off track.
Thanks for an accurate summation. Lincoln never claimed that the federal government was supreme in all areas. That didn’t come along till the Progressives of the late 19th century.