The song is a particular sweet number called "One Family," and it's from a show that Harnick wrote based on none other than...A Christmas Carol. Harnick is best-known for his work with composer Jerry Bock on such musicals as Fiddler on the Roof, She Loves Me and the Pultizer Prize-winning Fiorello! For this, though, he collaborated on the show with famed movie composer, Michel Legrand, who among many film scores wrote The Umbrellas of Cherbourg, as well as the original film version of The Thomas Crown Affair, for which he won an Oscar for the Best Song, "The Windmills of Your Mind."
Though their production of A Christmas Carol never was produced on Broadway, it's had a bit of a life in community theater. This number is sung in the show by the Cratchit Family, and it's performed here by Sheldon Harnick, along with his wife Margery Gray (who had a successful Broadway career, including the show Mr. Wonderful that starred Sammy Davis Jr., and oddly enough had music by Jerry Bock before he teamed up with Harnick), and Leigh Beery, who starred as Roxanna opposite Christopher Plummer in Cyrano, a musical adaptation of Cyrano de Bergerac. (She comes in with her main solo at the 1-minute mark. Margery Gray follows her.)
This (and the two that follow) come from the wonderful CD I've posted several selections from. Sheldon Harnick: Hidden Treasures, which you can find here.
These next two Christmas songs were written by Harnick and Bock for their musical She Loves Me (which is based on the Hungarian play that the movies Shop Around the Corner and You've Got Mail are adapted from). However, they're so little-known that people who even love She Loves Me inside-out likely don't even know them. That's because they were cut from the show.
The first song, "Christmas Eve," was to come at the very end of the show -- around the time when the "12 Days to Christmas" number, whose video I posted here the other day (12 days before Christmas) comes in. It's a lovely, wistful ballad, but in his liner notes Harnick writes that the song just didn't move the story forward enough and had to be taken out. It's sung here by the composers, with Harnick in the lead.
And the final number is probably best-described as a show song, one that really only fits within the context of the musical. Harnick notes that it was ultimately too complex and didn't work well-enough for that, so it too was cut. But it's good fun to hear, especially with Harnick filling in the dialogue. And if you do know the show, you'll recognize that some of the lyrics were saved and able to be used elsewhere in the show, mixed in as a sort of sardonic counterpoint in the song "Ilona." Here then are Hanick and Bock singing, "Merry Christmas Bells."