“A Very Murray Christmas” premieres Friday on Netflix.

In “The Judy Garland Christmas Show” of 1963, an early example of what soon became a genre, Garland has a duet with Mel Tormé. They sing “The Christmas Song,” which Tormé wrote with Bob Wells.

The song, with its evocative opening line — “Chestnuts roasting on an open fire” — had already been around for 18 years and was quite well known. Garland, though, who seems a bit fuzzy throughout the program, can’t quite get the words right. When she comes to the line about what Santa is hauling, she sings, “He’s load of lots of gifts and toys are in his sleigh.”

The essence of that moment is what Bill Murray is going for in “A Very Murray Christmas,” an hourlong special that has its premiere Friday on Netflix. He wants a Christmas special that seems just slightly off script, familiar, and recognizable yet also disturbingly wrong.

The result is a show that probably isn’t destined for repeat viewings but provides a few wry moments and even a listenable song or two. Murray, working with his “Lost in Translation” director, Sofia Coppola, and a guest list that includes Miley Cyrus, George Clooney, Chris Rock, and many more, doesn’t go the broad parody route taken by Dave Foley in “The True Meaning of Christmas Specials” (2002) or Stephen Colbert in “A Colbert Christmas: The Greatest Gift of All” (2008). But he doesn’t play it straight either. It’s a lot of homage, only a very low-key form of mockery, all of it served, it must be said, with too much self-indulgence.

The story, written by Murray, Coppola, and Mitch Glazer, works the bad-weather plotline of many Christmas specials of yore: Murray is distressed that a New York storm could prevent guests and audience from making it to his big holiday show.

“The airports are closed,” he laments. “The trains are closed. The buses and bridges and tunnels are not working. A couple of saloons have closed. The entire city of New York has shut down.”

Some of the guests who couldn’t make it to the party due to the snowstorm…

There are worse places to be stranded in a storm: Murray is at the Carlyle, and that hotel and its Bemelmans Bar and Café Carlyle provide the retro-cool settings for the special. Paul Shaffer is there with him, which gives “A Very Murray Christmas” its musical foundation, and eventually big-name guests materialize, either by accident (Rock just happens to wander by) or as worker bees or, eventually, in a high-dress fantasy sequence generated when Murray passes out.

The show demands a high tolerance for singing by people who aren’t singers, principally Murray in his lounge-lizard mode, but also Maya Rudolph. Cyrus and Jenny Lewis help counterbalance the off-key stuff, and anyway, the real point is in the eclectic song selection.

There are traditional Christmas numbers, done either genuinely or comedically. (Cyrus sings a decent “Silent Night”; a “Do You Hear What I Hear?” by Murray and Rock may have you reaching for earplugs.) But there are also numbers like the Pogues’ “Fairytale of New York.” And Murray and Clooney reach a level of ridiculous not seen since “Pee-wee’s Playhouse Christmas Special” when they combine on “Santa Claus Wants Some Lovin’.”

But that outlandish number is an exception. Every Christmas special has an overarching tone — saccharine, or wistful, or satirical — and “A Very Murray Christmas” corners the market on gloomy. It opens with Murray (wearing an antler headband) singing “Christmas Blues” and ends with Rudolph drinking alone. It tries hard — too hard, really — to turn melancholy into a thing, and it winds up being a holiday special for the disillusioned and dejected, full of inside jokes but in the end kind of empty.