Several years back there was a wonderful American Civil War game called No Greater Glory.
While the military side of the game at times seemed a bit off, what I really loved about that one was the way you had to watch the political side of things just as carefully as the military. I'm especially fond of this aspect because the North came very close to losing the war in 1864, even though they were clearly dominant on the battlefield -- i.e. if Lincoln had not been re-elected, his successor would have made peace with the South rather than trying to conquer it.
The most striking feature of the game was the need to play coalition politics: the leader had to keep the different political and geographical factions pacified by a giving a combination of cabinet posts and military commands to their adherents, regardless of competance or qualification. This produced some maddening military situations (large commands assigned to ineffective but influential generals) and some serious hairpulling when it came to handing out cabinet posts (keep your rival in you cabinet where you can keep an eye on him, or you'll find him running against you in the 1864 election). It was a very good thing that the American system does not include the Parliamentary no-confidence vote.
I mention this because most American Civil War games that I've seen since then have always concentrated on the military and, to some extent, the logistics. Logistics (and the naval war) are really important, and the American Civil war is a shadow of itself when you don't have to worry about sea lift, naval strategy, railroad infrastructure, and navigable rivers. But nothing can match the delight and frustration of being forced to make bad administrative and military appointments for political reasons, so I hope that any game covering this war will give full coverage to the political side.