We have 3 resident cats. I've been surprised that they aren't as bothered by Clownpup as much as they were when a new cat was brought home. The youngest, seems cautious, but intrigued and follows pup around. I think they even played together today.
The other two stay upstairs, but do walk around her. She follows them, but if they run she just turns around and does something else.
I read in one of the books about ensuring the cat isn't chased, using a training lead in the house, or always restraining the dog when introducing to the cat.
We have a massive cat tree thing (it goes to the ceiling) so they are happy to sit high up and watch her.
I think it can depend on the temperament of the cat and dog and breed.