Mountain dew is another term for poitín, an old Irish drink described for centuries as "Irish moonshine whiskey." It is the focus of the song "Good Ol' Mountain Dew," written by Bascom Lamar Lunsford (18821973), after which the soft drink was named:

There's a big hollow tree
Down the road here from me
Where you lay down a dollar or two.
Then you go around the bend,
When you come back again
There's a jugful of mountain dew.

Oh, they call it that old mountain dew
And them that refuse it are few.
Oh, I'll shut up my mug
If you'll fill up my jug
With that good old mountain dew.

Well, there's my old Aunt June
Bought some brand new perfume
It had such a sweet smellin' phew.
But to her surprise, when she had it analyzed
It was nothing but good old mountain dew.

And there's Uncle Mort
He's sawed off and short.
He's just five feet and one inch or two.
But he thinks he's a giant
When he gets him a pint
Of that good old mountain dew.

Now, there's Uncle Bill
Got a still on the hill
Where he runs off a gallon or two.
And the buzzards in the sky
Get so dizzy they can't fly
Just from smelling that mountain dew.

(Bascom Lamar Lunsford & Scott Wiseman)

There are many variations on the lyrics (anotherone's Mountain Drew writeup mentions more than a few). The song was said to be written after one of Lunsford's cases (he was a lawyer among many other things) in which he defended a moonshiner — he won the case by having the Judge taste the defendant's brew, to which the Judge ruled that anyone capable of brewing such a fine "dew" should not be in jail. The rights to the song were sold in 1937 to Scott Wiseman for $25 to buy a bus ticket. Wiseman revised the lyrics and it is now called one of the most famous folk songs ever.

I first heard of "Mountain Dew" as an alcoholic drink in another Irish song called "The Rare Ould Mountain Dew":

Let grasses and waters flow
In a free and easy way,
But give me enough of the rare old stuff
That's made near Galway Bay,
Come gangers all from Donegal,
Sligo and Leitrim too,
Oh, we'll give the slip and we'll take a sip
Of the rare old Mountain Dew

Hi the dithery al the dal, dal the dal the dithery al, al the dal, dal dithery al dee
Hi the dithery al the dal, dal the dal the dithery al, dal the dal, dal dithery al dee

There's a neat little still at the foot of the hill,
Where the smoke curls up to the sky,
By a whiff of the smell you can plainly tell
That there's poit´n, boys, close by.
For it fills the air with a perfume rare,
And betwixt both me and you,
As home we roll, we can drink a bowl,
Or a bucketful of Mountain Dew

Now learned men as use the pen,
Have writ the praises high
Of the rare poitín from Ireland green,
Distilled from wheat and rye.
Away with yer pills, it'll cure all ills,
Be ye Pagan, Christian or Jew,
So take off your coat and grease your throat
With a bucketful of Mountain Dew.

(From the Dubliner's Songbook 1974)

9 July 2003: Small edit thanks to CloudStrife.

I am not a lawyer. "The Rare Ould Mountain Dew" is in the public domain. I'm looking into my use of "Good Ol' Mountain Dew" and how it relates to fair use.