The phrase “root hog or die” means to get down to hard work or suffer the consequences, to shift for oneself.
The earliest literary use so far reported goes back only to 1834, to Davy Crockett’s autobiography, A Narrative of the Life of David Crockett, written just two years before his death at the Alamo.
It is likely, however, that this typical Americanism goes back to much earlier pioneering days.
It arose, undoubtedly, from the everyday observance of the fact that a hog, if left to forage for himself, is not in much danger of starving. He will root with his snout, or, to use another American term, he will “hog,” or appropriate greedily, whatever he can find in the nature of food.
It is possible, of course, that the original sense was a command, as it were, to a hog to start rooting or suffer death. But in the use that we have always heard “hog” had merely the force of a verb, one of a triplet, “to root, hog, or die”, just as the phrase, “eat, drink, and be merry.”