If you don't mind. All you've provided so far is the same quote from the same website twice. All that website does is provide a third party version of the Stephens quote, something you felt free to criticize in reply 57. The link I provided at least gives some context.
The relevent material consists of one paragraph and a footnote to it. They are as follows:
Other matters were then talked over relating to the evils of immediate emancipation, if that policy should be pressed, especially the sufferings which would necessarily attend the old and the infirm, as well as the women and children, who were unable to support themselves. These were fully admitted by Mr. Lincoln, but in reference to them, in that event, he illustrated all he could say by telling the anecdote, which had been published in the papers, about the Illinois farmer and his hogs.* The conversation then took another turn.
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*Mr. Lincoln had a wonderful talent for illustrations of this sort. His genius for Anecdotes was fully equal, if not superior, to that of Æsop for Apologues or Fables. They were his chief resort in conveying his ideas upon almost every question. His resources for producing them, seemed inexhaustible, and they were usually exceedingly pointed, apt, and telling in their application. The one on this occasion was far from being entitled to a place on a list of his best and most felicitous hits of this character. The substance of it was this:
An Illinois farmer was congratulating himself with a neighbor upon a great discovery he had made, by which he would economize much time and labor in gathering and taking care of the food crop for his hogs, as well as trouble in looking after and feeding them in winter.
"What is it?" said the neighbor.
"Why, it is," said the farmer, "to plant plenty of potatoes, and when they are mature, without either digging or housing them, turn the hogs in the field and let them get their own food as they want it."
"But," said the neighbor, how will they do when the winter comes and the ground is hard frozen?"
"Well," said the farmer, "let 'em root!"
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The book is titled: "A Constitutional View of the Late War Between the States: its Causes, Character, Conduct and Results" by Alexander H. Stephens. The copy I have is a modern reproduction (Sprinkle Publications, Harrisonburg, VA).
The material quoted above is from vol. II, p. 615. The context is a discussion of the proceedings of the Hampton Roads Peace Conference of February, 1865.
Stephens' dedication in volume II is dated April 26, 1870, and there is what appears to be a copyright notice dated 1870.
The song "Root hog, or die" dates to 1856, according to what I found on the web, but as you can see, Stephens makes no mention of it.