"Root hog, or die" is a common American catch-phrase dating from well before 1834. Coming from the early colonial practice of turning pigs loose in the woods to fend for themselves, the term is an idiomatic expression

Idiom

Idiom is an expression, word, or phrase that has a figurative meaning that is comprehended in regard to a common use of that expression that is separate from the literal meaning or definition of the words of which it is made...

for self-reliance.

"Root Hog Or Die" (c. 1854)

Several songs of unknown authorship were published before the Civil War, including patriotic and minstrel songs. A patriotic version opens with:

I'll tell you a story that happened long ago,

When the English came to America, I s'pose you all know,

They could'nt whip the Yankees, I'll tell you the reason why,'

Uncle Sam made 'em sing Root Hog or Die.

"Root, Hog, or Die" (1856)

The most popular song of the era was a minstrel song variously titled "Root, Hog, Or Die" or "Do Jog Along", sometimes credited to George W.H. Griffin, which was first copyrighted in 1856. Many variations exist—a common first verse is:

I'm right from old Virginny wid my pocket full ob news,

I'm worth twenty shillings right square in my shoes.

It doesn't make a bit of difference to neither you nor I

Big pig or little pig, Root, hog, or die.

"Root Hog Or Die" (1858)

A song from the gold field camps on the front range of the Rockies written by G.W.H. Griffin in 1858 addressed the hardships of gold miners. The first verse:

Way out upon the Platte near Pike's Peak we were told

There by a little digging we could get a pile of gold,

So we bundled up our clothing, resolved at least to try

And tempt old Madam Fortune, root hog or die.

Civil War songs

Both sides in the Civil War had root, hog, or die songs. A verse from "Flight of Doodles", a Confederate song, is typical:

I saw Texas go in with a smile,

But I tell you what it is, she made the Yankees bile;

Oh! it don't make a nif-a-stifference to neither you nor I,

Texas is the devil, boys; root, hog, or die.

"A Philosophical Cowboy"

A folk song collected in 1911 tells of the hard life of the cowboy. The last verse is:

Sometimes it's dreadful stormy and sometimes it's pretty clear

You may work a month and you might work a year

But you can make a winning if you'll come alive and try

For the whole world over, boys, it's root hog or die.

This version, and variations of it, are still recorded.