Many of our modern methods of campaigning would astonish and confuse the Presidents of yesteryear. Martin van Buren never ate a fried corn dog at a state fair. But times change!
In the early 1900s a stuffed bear named after Theodore Rooselvelt became popular. This was because Roosevelt had refused to shoot a bear tied to a tree. The supporters of his successor William Howard Taft decided that Taft needed a counterpart to this Teddy Bear, and they settled on a possum. This was because Taft ate one.
Sadly, this more or less ends the history of Presidential campaign mascots. Your mission is to prolong that history, and make campaign mascots an obvious inclusion in any modern campaign. And I don't mean like the Democratic donkey or GOP elephant, these are named characters associated with specific people.