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?
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.
I don't fault Lee at all. He was a general, not a politician. This is one of the reasons the Constitution specifies that the military must be subordinate to the civilian power - one cannot expect military specialists to be capable of dealing with the political aspects of war. That was Davis' job, and *he* fumbled it badly, IMO.