According to the military conventions of that time(and today, I believe) 2 to 1 advantage in nmbers was not considered to be an overwhelming force and, if that is the case, then Lincoln with a numerical advantage, but, not an overwhelming one, then the war was Lincolns to lose rathern than Davis to win.
The geographic scale over which you have a 2:1 advantage matters, though. And Clausewitz held that between two forces of fundamentally similar baseline quality it would be very hard indeed to win at 2:1 odds - he can only find a couple of examples in more than a century.
Clausewitz:
Here we find armies much more like one another in equipment, organisation, and practical skill of every kind. There only remains still alternately a difference in the military virtue of armies, and in the talent of generals. If we go through the military history of modern Europe, we find no example of a Marathon.
Frederick the Great beat 80,000 Austrians at Leuthen with about 30,000 men, and at Rosbach with 25,000 some 50,000 allies; these are however the only instances of victories gained against an enemy double, or more than double in numbers. Charles XII., in the battle of Narva, we cannot well quote, the Russians were at that time hardly to be regarded as Europeans, also the principal circumstances even of the battle, are but too little known. Buonaparte had at Dresden 120,000 against 220,000, therefore not the double. At Collin, Frederick the Great did not succeed, with 30,000 against 50,000 Austrians, neither Buonaparte in the desperate battle of Leipsic, where he was 160,000 strong, against 280,000, the superiority therefore considerably less than double.
From this we may infer, that it is very difficult in the present state of Europe, for the most talented general to gain a victory over an enemy double his strength. Now if we see double numbers, such a weight in the scale against the greatest generals, we may be sure, that in ordinary cases, in small as well as great combats, an important superiority of numbers, but which need not be over two to one, will be sufficient to ensure the victory, however disadvantageous other circumstances may be. Certainly, we may imagine a defile which even tenfold would not suffice to force, but in such a case it can be no question of a battle at all.