Another version of this came to my ears recently. The melody has one or two noticeable differences, though it's out of the same family. The chorus is very similar to "Hard, Ain't It Hard," and it's quite possible the Acuff recording was the direct inspiration for the Guthrie version.

One Old Shirt
as sung by Roy Acuff and His Smoky Mountain Boys, Vocalion 04657 (1938)

One old shirt is all I've got
And a dollar is all I crave
Oh, I brought nothing to this whole wide world,
Gonna take nothing to my grave.

(chorus)
Oh, ain't it hard, hard, oh, Lord, ain't it hard
To love a girl that don't love you?

Now come, my little pink and tell me what you think
You're a long time making up your mind.
Oh, you tell more lies than the stars in the skies,
Sweet baby, your heart's not mine.

My baby come home late hours in the night
She just keeps rapping on the door
I wake up in my stocking feet
My baby don't rap no more.

[Or perhaps the last line should go
My baby, don't rap no more. Acuff doesn't sing a noticeable comma in it, though.)

I love you, sweet baby, till the sea runs dry
The rocks are at the sun
I love you, sweet baby, till the day I die
Then you may know I'm gone.

I wish I was on some rocky mountain top
Sitting in my big armchair
With one arm around my liquor keg
And the other one around my dear.