I've gone on the record many times about my dislike of pop Christmas music, particularly those songs that are really love songs or break-up songs or . . . greed songs, that do not have anything to do with the religious holiday that is supposed to be the whole point of the enterprise.
"Santa Baby" is just such a song - its basically a song about a gold digger, and just uses Christmas as a way in. Also, it turns the otherwise-perfectly-find word "chimney" into a euphamism for "vagina."
Having said all of that . . . I don't mind this song when Alison Brie sings it, because Alison Brie is perfect. She has important roles in the best drama (Mad Men) and the best comedy currently on television (Community). And she's adorable. So, um, you may want to check this out: