Not that Lincoln's relationship with his own generals was much better during most of the war, but you're right. This is something frequently lost in more romantic analysis of the war.
If I recall, after losing command of the main Confederate Army around Richmond (soon to gain renown as The Army of Northern Virginia under General Robert E. Lee) due to a bullet wound, Joe Johnston bitterly commented that the bullet that struck him was the most fortunate thing that could have happened to the Confederacy. Not that Johnston thought Lee was a better general than himself. He didn't think so at all. But he noted, accurately, that Lee would be more effective because he had the confidence of the president (Jefferson Davis) while he did not.
If Ol' Joe could have held onto Atlanta until after the federal elections of '64, the Confederacy could have won by Lincoln losing to McClellan. Other than that, by that time in the war, I don't see any way that the Confederacy could have pulled out a victory.