Lincoln related the circumstances behind the story in to Alexander McClure.
"You see," said he, "we had reached and were discussing the slavery question. Mr. Hunter said, substantially, that the slaves, always accustomed to an overseer, and to work upon compulsion, suddenly freed, as they would be if the South should consent to peace on the basis of the 'Emancipation Proclamation,' would precipitate not only themselves, but the entire Southern society, into irremediable ruin. No work would be done, nothing would be cultivated, and both blacks and whites would starve!"
Said the President: "I waited for Seward to answer that argument, but as he was silent, I at length said: 'Mr. Hunter, you ought to know a great deal better about this argument than I, for you have always lived under the slave system. I can only say, in reply to your statement of the case, that it reminds me of a man out in Illinois, by the name of Case, who undertook, a few years ago, to raise a very large herd of hogs. It was a great trouble to feed them, and how to get around this was a puzzle to him. At length he hit on the plan of planting an immense field of potatoes, and, when they were sufficiently grown, he turned the whole herd into the field, and let them have full swing, thus saving not only the labor of feeding the hogs, but also that of digging the potatoes. Charmed with his sagacity, he stood one day leaning against the fence, counting his hogs, when a neighbor came along.
"'Well, well,' said he, 'Mr. Case, this is all very fine. Your hogs are doing very well just now, but you know out here in Illinois the frost comes early, and the ground freezes for a foot deep. Then what you going to do?'
"This was a view of the matter which Mr. Case had not taken into account. Butchering time for hogs was 'way on in December or January! He scratched his head, and at length stammered: 'Well, it may come pretty hard on their snouts, but I don't see but that it will be "root, hog, or die."'"
Lincoln was talking to one of the Confederate commissioners, Hunter. Hunter was expressing his concern about what would happen to southren society without the slave labor that provided their wealth. Without slaves, Hunter complained, no work would be done. Nothing would be harvested. People would starve. So when Lincoln related the story it was to point out that the white population could no longer live off the labors of their chattle. The white population would have to work for a change. It was the white population that would have to 'root hog, or die' not the former slaves.
Lincoln, unlike modern south-haters, knew that only a small precentage of southerners owned slaves. Work was nothing new to the white population of the south, but that claim does have a continued popularity among the culturally marxist.
From the Abraham Lincoln Association via University of Illinois --
From another issue of the Journal of the Abraham Lincoln Association, also published by the University of Illinois --
This anecdote, which appears in both Stephens and Campbell's accounts and which Lincoln later repeated to his portraitist, reveals a harsh side to Lincoln, perhaps caused by his desire to reassure the Confederates that he did not seek a social revolution in the postwar South. The story also belies Lincoln's earlier expressions of sympathy for black refugees from slavery and his approval, one month after the Hampton Roads Conference, of the Freedman's Bureau bill providing temporary aid for the former slaves (and white refugees) in their adjustment to freedom. Still, Lincoln, like most Americans at the time, optimistically expected emancipation itself to be "the king's cure" for blacks in the South. Lincoln believed that a free person, now including blacks, should be able to make his way in America through his own ability and effort without the assistance of the state. Though he had admitted the difficulties of the white and black races living together in freedom (his earlier support for black colonization reflected this concern), the president envisioned a limited role for the federal government in protecting and aiding blacks after the war. Had he lived to witness the postwar threat to black freedom, Lincoln might have changed his mind regarding federal responsibility for black liberty.
It's a good article on the Hampton Roads meeting. I recommend it.