tar + baby, from African American folklore, popularized by the tale of Br'er Rabbit in the Uncle Remus stories (1881) of Joel Chandler Harris, originally from Cherokee folklore (a tar baby story was published in the Cherokee Advocate, 1845).
tarbaby (plural tarbabies)
- A difficult or "sticky" situation, especially one where peoples' attempts to make it better only make it worse
- (pejorative, ethnic slur) A black person
Usage notes 
The term is easily construed in the offensive, pejorative sense, and thus it is prudent to avoid it, instead referring to a “sticky situation”.