Another post on the Disunion blog quotes Senator Alfred Iverson of Georgia in his farewell speech to the Senate during the secession crisis.
Iverson estimates that the North's "conquest [of the South], if you gain one, will cost you a hundred thousand lives, and more than a hundred million dollars. Nay more, it will take a standing army of 100,000 men, and millions of money annually, to keep us in subjection."
This certainly closer to the truth than Edmund Ruffin's estimate that appeared in an earlier post on which I commented. But it's still pretty far below the true cost borne by the North, let alone the total cost to the nation.
UPDATE: And here's another cost estimate on the Disunion blog.