Amy Poehler, Bill Murray and Julie White in the Netflix original holiday special “A Very Murray Christmas.” (Ali Goldstein/Netflix)

Among its other uses, the televised Christmas special once provided such delightful target practice for critics (a little Kathie Lee Gifford, anyone?). In years since, picky viewers have learned to ignore the few specials that remain, such as NBC’s annual, forced-cheer broadcast from the Rockefeller Center tree-lighting.

Someone is always willing to try again, usually by unpacking the old tropes of holiday specials. They do them retro-style, with tongue planted firmly in cheek and eyes widened at the sound of the doorbell, which signals the arrival of another celebrity guest covered in pretend snowflakes. And who does tongue-in-cheek better than Bill Murray?

That is essentially the premise behind Netflix’s one-hour “A Very Murray Christmas.” Co-written and directed by Sofia Coppola (who coaxed such a memorable performance from Murray in the 2003 film “Lost in Translation”), the special isn’t as funny or inventive as one might hope. The set-up is cheesily self-aware: Murray, in his familiar lounge-lizard mode, is trapped in the Carlyle Hotel during one of those intense Manhattan blizzards that probably will not exist in the near future, after a few more glaciers melt in the bourbon glass.

He is supposed to perform in a live TV Christmas special from the hotel’s famous stage, but the snow has all but shut New York down and none of his guest stars can make it — not even George Clooney.

Pressured by his agents (Amy Poehler and Julie White) to go on with the show to which he is contractually bound, Murray is rescued when the power fails a few minutes into the broadcast — as he is singing a duet (“Do You Hear What I Hear?”) with last-minute, reluctant help from Chris Rock.

Murray and his piano player (Paul Shaffer) retreat to the bar, where lonely guests and unoccupied hotel staff congregate — and sing! — which means more cameos. Musician Jenny Lewis plays a cocktail waitress; David Johansen is a bartender. Jason Schwartzman and Rashida Jones play a couple whose wedding was canceled by the snow (Murray eggs them on to sing Todd Rundgren’s “I Saw the Light”), and the French pop band Phoenix plays the kitchen staff — and performs another song.

It is all passably entertaining; Coppola keeps things somewhat morose until Murray passes out drunk and dreams himself into a proper TV variety-show idea of the winter wonderland soundstage: Clooney and Miley Cyrus arrive by sleigh (she belts out a pretty good “Silent Night”), and before you know it the hour has elapsed.

Yet it never feels exactly right. This might be a technological matter that, for once, gives the advantage to old-fashioned television — the kind you plug in the wall and watch according to its schedule, not yours. Netflix can do many things that broadcast TV cannot, but whatever ineffable irony is left to squeeze out of the Christmas special just doesn’t translate here. Cheers, anyhow.

A Very Murray Christmas (one hour) available Friday on Netflix.