Americans in general don't embrace animal abuse. Cock-fighting is illegal in most of the US too. The Federal Government can't make it illegal, but I believe all States and Territories except Puerto-Rico have outlawed the practice.
And that is not a political thing at all. It's one area where democrats and republicans generally agree.
EDIT: Not being able to eat dogs is a purely cultural thing. There are few species that we routinely consider pets that you can also legally order at a restaurant. Rabbits are the only one that comes to mind. Some of the squeemishness over eating dogs might comes from their high intelligence within the animal kingdom, but that certainly doesn't stop monkeys from becoming food in a number of places and in a small part of Japan they routinely (but illegally) kill dolphins. It's still not a political party thing.