Clues to the origin of "going to hell in a handbasket," meaning "deteriorating rapidly or utterly," are, unfortunately, scarce as hens' teeth. The eminent slang historian Eric Partridge, in his "Dictionary of Catchphrases," dates the term to the early 1920's. Christine Ammer, in her "Have A Nice Day -- No Problem," a dictionary of cliches, agrees that the phrase probably dates to the early 20th century, and notes that the alliteration of "hell" and "handbasket" probably contributed to the popularity of the saying. Ms. Ammer goes a bit further and ventures that, since handbaskets are "light and easily conveyed," the term "means going to hell easily and rapidly." That seems a bit of a stretch to me, but I do think the addition of "in a handbasket" (or "in a bucket," as one variant puts it) does sound more dire and hopeless than simply "going to hell."