A Tarbaby is a beautiful tortoiseshell cat with golden eyes who loves to chirp and chortle. Though often sweet and affectionate, they are easily irritated and will often whine when they are displeased.
A dummy made of tar, which cannot be struck without getting oneself hopelessly stuck to it--from the story "Mr. Rabbit and Mr. Fox" by Joe Harris, as told by his fictional narrator, Uncle Remus.
Tar baby has become short hand for a situation better avoided than confronted.
The issue of immigration has become a tar baby for president Gearge W. Bush.