Therein lies the origin of my claim that the South (and in particular, Jefferson Davis) blew it.
The South could never have defeated the North militarily, with the disparity of resources and manpower. However, they could have obtained a truce, and their independence, by the means you suggest, if they had pursued such as a strategy from the very outset.
The fatal error was Davis' allowing Lee to invade the North. That solidified Northern opposition, as well as getting Lee defeated at Gettysburg. If the South had restrained itself as a political and military strategy, and waged a defensive war from the outset, it could have positioned itself politically in world opinion as a beleaguered, injured party, and remained militarily on the defensive, concentrating on chewing up the Union armies whenever they tried to advance. By conserving their forces in this manner they could have bled the Union in such a way that the mommies at home would have started whining for peace. My belief is that the two political objectives of swaying the elections in the North to replace Lincoln with someone who would have sought an accomodation with the South, and obtaining diplomatic recognition (and possibly military support) from the British and other European countries, would then have succeeded.
But any such strategy would have required a civilian commander of far more stature than Davis - one with the iron will to restrain Lee, and the philosophical sophistication to understand the South's position from a historical perspective.
However, you are right in your idea that Davis was fatally wrong for his position, particularly in his dealings with Lee. Lee was by nature an aggressive fighter, though also a fine defensive tactician, and had he been under a president commited to aggressive warfare, he perhaps would have crushed the Union armies. However, Davis lacked the will to decide between a defensive war and an aggressive war- he tried to play both cards, and it hardly worked. At times he instated aggressive commanders when the precise opposite was needed- witness his replacement of Johnson with Hood. He rarely recognized the capabilities of his generals, and often neglected them at prime opportunities.
Personally, I find the methods of N.B. Forrest to be some of the finest implemented by the Confederacy, considering their situation. Forrest was capable of excellent defense, holding eastern Mississippi and Alabama quite well until 1865, and conducting swift and well-executed raids upon enemy position in occupied states. He operated with fairly minimal numbers and was usually very under-armed, yet, even when opperating against vastly superior numbers he tended to hold the upper hand and rarely lost a battle, or suffered heavy losses (there were exceptions, of course, the most notable- and perhaps embarrasing- at Parker's Crossroads, TN). Had he been given greater liberty to strike at, say, Sherman's line of supply, the results for the Confederacy would have been excellent.
It was Sumter that quickened the North's anger and strengthened its resolve.
Gettysburg and Antietam did help to bolster flagging Union determination, but so did Vicksburg, Mobile and Atlanta. Victory over an invader was better for morale than victory in enemy territory, but it's victory that was most important. Had Lee won at Gettysburg, would that have increased Northern determination?
Lee's aggressive tactics and willingness to incur losses hurt his side, but these were as much in evidence on his own territory as in enemy country.
You could make a case against those tactics and argue that a far more defensive style of war more focused on avoiding losses would have served the Confederacy better.
In defense of Lee, his way of fighting was intended to offset Confederate losses in the West, to rouse failing morale, and to convince outsiders that the Confederacy had become a viable nation. He was looking for the master stroke, perhaps because fatalism convinced him that Northern numbers and industry would otherwise prevail.
And flushed by some of their victories in the East, "writing off" the border states and territories was something Confederate leaders would not do. In some very real ways, we are talking about a revolution and an empire when we talk about the Confederacy. It's only in retrospect that its victim status predominates.
So yes, Lee could have behaved differently and perhaps have succeeded over time, but only if the Confederacy had had good enough commanders in the West -- which they didn't have. If rebel commanders in the West had prevented their domain from being divided, a more conservative strategy could also have been pursued in the East, and perhaps over time Unionists would have grown weary with the long war.
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The war must have seemed very strange and absurd to many Americans before the horror sank in. In so many ways we were clearly one country then, perhaps more so than we are today. Of course had the Confederacy succeeded we would see things differently. But for Americans living before or after the conflict it would have seemed inconceivable or inexplicable. Those who tell us that leaving slavery out of the picture makes things clearer are wrong, as it makes secession and war so much more incomprehensible.
The idea of the rebellion as a libertarian revolt may jibe with current political preoccupations, but how valid is it? Would putting what would probably be an armed and fortified international border on the Potomac or the Ohio or the Mason-Dixon line lessen the role of government in American life?