root hog, or die was used by Davy Crockett, 1834.
"We therefore determined to go on the old saying root, hog, or die."
The Dictionary of American English; "A Narrative of the Life of Davy Crockett."
Some record of its usage before the 1830s should be found, if it was an "old saying."

An Iowa agricultural report for 1866 was to turn out pigs into the woods or prairies to get their own living. This practice started with early hog farmers.

John D. Wright, in "The Language of the Civil War," wrote that it meant you had to create your own shelter or die.

The first use of the phrase in song that I can find is in minstrel shows in 1856.

Additions, anyone?