There was a cartoon when I was kid with a character called Possum Puss. I remember another character speaking his name in a hillbilly drawl. I thought it might have been Cattanooga Cats, but I just watched an episode on YouTube and it didn’t have that character. (Although it did have the Scoots cat say ‘Wavy Chitlin Gravy’. I didn’t know who Wavy Gravy was when I was a kid, so the joke went over my head like a trapeze act.)
Anyone remember Possum Puss?
I’ve never heard of Possum Puss, but Hanna-Barbera did have a Punkin Puss.
I bet you are thinking of Punkin’ Puss & Mushmouse from the Magilla Gorilla show.
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Jim
Aha! It would have been easier to find if I’d remembered the name correctly.
Damn, **mobo85 ** is quick. His post was not there when I previewed mine. That’s what I get for adding an extra link. 
Although it’s already been answered, there was also “Putty Puss,” from The Houndcats.
I think you’re thinking of Possible Possum, a drawling hillbilly critter whose tagline was “It’s possible! It’s possible!” He was a supporting character in Terrytoons’ Deputy Dawg cartoons.
I remember Musky with that line.
Also Dick Tracy.