A dog catcher (or dog warden or animal control officer) is an employee of, or a contractor to, a municipality, charged with catching stray or loose dogs, cats, and sometimes other animals, and bringing them to a compound or animal shelter, where the animals are held for a certain time before being returned to their owners, put up for adoption, or killed.
In some localities, the dog catcher is an elected office, generally considered the very lowest such office possible. For that reason, the phrase "I wouldn't vote for him for dog catcher" entered the language as meaning a politician who is so bad that the speaker wouldn't even vote for him for the least significant position of trust.