"Going to hell in a handbasket", "going to hell in a handcart", "going to hell in a handbag", "go to hell in a bucket", "sending something to hell in a handbasket" and "something being like hell in a handbasket" are variations on an American allegorical locution of unclear origin, which describes a situation headed for disaster inescapably or precipitately.

Based on this passage, what does it mean to go to hell in a handbasket? Let's give stream of consciousness first:
To answer the question, consider the following: "Going to hell in a handbasket", "going to hell in a handcart", "going to hell in a handbag", "go to hell in a bucket", "sending something to hell in a handbasket" and "something being like hell in a handbasket" are variations on an American allegorical locution of unclear origin, which describes a situation headed for disaster inescapably or precipitately.
So, the final answer is a situation headed for disaster inescapably or precipitately.