Isn’t that “The Ventures”; if so, they have a bunch of Christmas songs.
–“Fuck Christmas” by Fear 
–“Christmas Card From A Hooker In Minneapolis” by Tom Waits
–“Christmas in Prison” by John Prine
Some jazz instrumentals
–“My Favorite Things” by John Coltrane (I know “My Favorite Things” isn’t really a Christmas song but it’s often played this time of year so why not go with Coltrane’s version)
–“We Three Kings” by Miles Davis
Of course it is! Spellcheck doesn’t really work for band names.
“A Podsafe Christmas Song” by Jonathan Coulton.
Biggirl, last year’s Christmas mix kicks ass - hopefully I can go find all of that on iTunes.
Lute, you fucking rock!
Good one, but I like Robert Earl Keen’s original better. 
My fave alternative Xmas songs would be (in no particular order);
“I Believe in Father Christmas” - Emerson, Lake and Palmer
“Walking 'Round in Women’s Underwear” - Bob Rivers
“Porky Pig’s Blue Christmas” - Mark McCollum
“Mistress for Christmas” - AC/DC
“I’ve Got Some Presents for Santa” - Sarah Taylor (Lyrics by Billy Mumy)
You’ve listed everything else I can think of.
A couple I just thought of, not yet mentioned in this thread:
“Oi to the World” by the Vandals (though I prefer No Doubt’s cover version)
“The Rebel Jesus” by Jackson Browne
“Please Don’t Shoot Me, Santa” by the Killers
“Please, Daddy (Don’t Get Drunk This Christmas)” by Alan Jackson
I think all but two in my list are on my iPod.
Oh, and “Frosty the Snowman” from the Jack Frost soundtrack. Best part of the whole movie.
Dar Williams’ song “The Christians and the Pagans” talks about a Christmas dinner where the relatives invite the family’s black sheep niece, even though she and her partner celebrate Solstice instead. It is warm and fuzzy but should fit well on the tape.
Just had “Noel! Noel!” by Eve 6 come up on my iPod.
Just saw Joni Mitchell’s “River” in the Depressing Christmas Songs thread. I have the version by Robert Downey, Jr.
If you liked the Ventures version of Christmas, give a listen to Los Straitjackets "“Tis the Season for Los Straitjackets!” album. Its the surf version take on holiday favorites as perfomed by four men in Mexican wrestling masks. A must own.
I’ll add “Santa’s Beard” by They Might be Giants to the mix - nothing like some fun, philandering Santa to warm the cockles of your heart.
Also, I’ve got a truly amazing version of “Silent Night” by Tom Waits. It’s pretty much the normal song, so I don’t know if it qualifies for your mix, but the voice makes it pretty unusual. He does some gorgeous harmonizing. It’s my favorite xmas song hands down.
Re. “Santa’s Beard” – would that be the facial hair, or Mrs. Claus? Enquiring minds…
I’ve already got most of the songs mentioned and there are about 5 more i’m going to download when I get home for my christmas party but here are a couple not mentioned:
“five pound box of Money” Michelle Wilson
“gift of the Magi” Squirrel Nut Zipper
“Indian Giver” Squirrel Nut Zipper actually the whole CD is great
“Gary the Green Nosed Reindeer” MC Lars
“Christmas Night of Zombies” MXPX
“I saw Daddy Kissing Santa Clause” Stand Still
Another good one just came up in a podcast I get: “Hating You For Christmas” by Everclear. (It’s an unlisted track on So Much for the Afterglow.)
I found an MP3 of “Hooray for Santa Claus” as heard in Santa Claus Conquers the Martians.
I just wanted to come in to mention that I was listening to the original at work today. It’s been awhile since I listened to it, and forgotten what was on it. When the first song came on I was reaaaaaaaaally happy that I have a door on my room.