The tune and versions were certainly known to the miners in California.
I will post "Then Hurrah for Home," Put's Golden Songster, 1858,in a separate thread. It uses the melody.
"Few Days" was issued as solo piano music in 1855 (American Memory) and also for the guitar. Both American Memory and Levy Sheet Music have copies of the political versions, and the song was printed in folios of minstrel songs in the 1850s.

Here is a temperance (and post-Civil War) version, written and published by John A. Stone in SanFrancisco, 1867.

FEW DAYS (Temperance Banner)
John A. Stone

Our country now is great and free
Few days, few days,
And thus shall it forever be.
We know the way,
Though rummie foes may gather here,
Few days, few days,
We will protect what we hold dear.
We know the way!

Chorus:
We'll battle innovation,
Few days, few days,
And fight against usurpation
By a cunning foe.
For our guide's the Temp'rance banner,
Few days, few days,
Our guide's the temp'rance banner,
We know the way.

The world shall see that we are true,
Few days, few days,
And that we know a thing or two,
We know the way!
As temperance men go hand in hand,
Few days, few days,
Our countless throng shall fill the land
We know the Way!
Chorus: We'll battle inovation, [c?].
Then shout aloud. o'er hill and plain,
Few days, few days,
We will Temperance rights maintain,
We know the way!
We'll always guard it with our might,
Few days, few days,
And keep it steadfast in the right,
We know the way!
Chorus: We'll battle inovation, [c?]

From John A. Stone, "The California Temperance Song Book," p. 46, San Francisco, 1867. This was a copy from the song book, at American Memory, and seems to be incomplete.

In the decade 1860-1870, the population of San Francisco jumped from 56,000 to 160,000, the 10th largest city in the U. S. at the time, and a mercantile center.
John Stone was keeping up with the times; temperance songs rather than songsters about miners and Hangtown Gals.