Animals that better represent them, especially since the origins of each aren't particularly inspired anyway (the donkey was picked for the meme because people called Jackson a jackass and the elephant was picked because everyone was ignoring 'the elephant in the room' or something, I was too bored to read further).
I'm open to ideas, but here are my suggestions:
Republicans: Wasp. The wasp is the big bad asshole of the ecosystem. It stings foes, it stings friends, it stings neutrals. It stings anything it can point its ass at except other wasps. It's a being of pure hate, angry from the moment it's born and desperate to make sure nobody is having a good time anywhere it goes.
Democrats: Chihuahua. The chihuahua is a shivering little asshole that likes to act tough and hard until it faces any opposition whatsoever. Then it yelps and runs away with its tail between its legs. It has a big bark but very little bite both figuratively and literally. Not the kind of dog that should be protecting the home. But you bring it home anyway because hey, at least it's not a wasp.
Also, we need a new party. Is green taken? Their mascot could be the T-rex. How do we make this happen?
There's a time and place for everything... but not now.