Wikipedia
Tar-Baby
The Tar-Baby is a fictional character in the second of the Uncle Remus stories published in 1881; it is a doll made of tar and turpentine used to entrap Br'er Rabbit. The more that Br'er Rabbit fights the Tar-Baby, the more entangled he becomes.
In modern usage, "tar baby" refers to any "sticky situation" that is only aggravated by additional involvement with it.