This doesn't sound like it was meant to be a parody of TENNESSEE STUD. Although the structure is similar, the tune is different.
IDAHO SPUD As recorded by Dennis Coats on "Coats String Band" (2011)
Along about 1975, I left LA., barely left alive, An' I like a Texan chewin' his cud, I traded my tent for the Idaho spud, Traded my tent for the Idaho spud.
Out on the highway, thumb in the air, I got me a whiff o' that Idaho air. After a while, it gets in your blood, Walkin' an' talkin' like an Idaho spud, Walkin' an' talkin' like an Idaho spud.
CHORUS: Hey, the Idaho spud's a small fry's dream: 'Taters, 'skeeters, a big trout stream. You take the smog; we'll take the mud. We'll get along on the Idaho spud. We'll get along on the Idaho spud.
I got a sixty-three pickup, a cool wop(?) cap, Headed for town with a Bible in my lap. Shaved the hair off the back o' my neck. I blended right in like a 'tater sack, Blended right in like a 'tater sack.
Yeah, I met a little girl with a gleam in her eye, Took her hand and I told her that I 'D never let her go if she took me in. Together we're a-livin' on 'tater skins. Together we're a-livin' on 'tater skins.
CHORUS
Up on the mountaintop cuttin' me some trees, I met me a bear with a case o' hungries. I thanked the Lord in heaven above I had a twenty-pound bag of my Idaho spud, Twenty-pound bag of my Idaho spud.
Well, my truck stopped runnin' and my gas was all gone. I grabbed my 'taters and I mashed till dawn, Opened up the tank, I poured in the suds. I made it on home on the Idaho spuds. I made it on home on the Idaho spuds.
CHORUS Oh, we'll get along on the Idaho spud. Hey, we'll get along on the Idaho spud.