IMHO they should use the Grey Wolf as the symbol of the Patriot party. I love eagles but that is the nations bird. There is a reason GOP and Dems use donkey and elephant. Normally I'd say lion because it looks cool and its not like elephants are native to the USA. However the grey wolf is a pack animal and is one of the most tenacious survivors on the planet.

Unlike the donkey or the elephant its also an apex predator. Brown bears are the only thing that even argues with a large wolf pack.

https://en.wikipedia.org/wiki/Wolf#Interactions_with_other_predators

Plus similar artwork to the donkey and elephant would be easy to make with a wolf. Most notably put 2-3 (or even 4 or 5) in the artwork to show its not some lone wolf... we are an entire pack of wolves.