Don’t cross pugs and American cockers!
There is already a breed for you!
In America, we call this breed an English toy spaniel. In the rest of the world, it’s called a King Charles spaniel, because both Stuart kings with the name of Charles had these dogs. (But they had longer muzzles and were not far removed from red and white sporting spaniels.)
These dogs became pug-nosed at some point in the late nineteenth century. Lots of sources point to Japanese chin blood, which could have played a part, but I don’t think it was the primary source. There is some evidence that toy bulldogs and pugs were crossed in.
The Cavalier King Charles spaniel, which is now much better known, was created as an attempt to bring back the dogs of the House of Stuart– to overthrow the Roundheads once again!
Of course, the creators of the Cavalier chose too narrow a gene pool to start their breed, and as it can easily be argued that the Cavalier is a breed failure. Its levels of genetic load far exceed what most people would consider acceptable.
But the pug-nosed English toy spaniel shows what would happen if we began breeding for extreme brachycephaly in gun dogs.
We could do it.
But I don’t think we should!