Well, I think 1:2 should be more than enough for CSA to stay even with USA, but against human opponent good luck getting that
Once again, battle losses are only part of the picture. Starving can lead to enormous losses, but those will not be registered. Soldiers lost with elements remaining intact are "cheaper" to replace than the same number of soldiers with their elements completely annihilated. Fixed units are more acceptable losses than ones you can move. Losing some soldiers in the field is better than, say losing an important fort.
As CSA, unless you are dominating your opponent, you are on the defensive, taking offensive only in order to prevent enemy from concentrating his forces and crushing you or to exploit opportunities that arize (sudden death due to capturing Washington :thumbsup

Ratio of 2:1 in USA favour, but overall losses being small and strategic cities remaining in CSA hands is far better than 1:1 ratio with massive magnitude of losses.