What I found after a brief search with Google Scholar is that chihuahuas and Great Danes are unlikely to breed naturally, but I found nothing reliable that said it was impossible. They are mutually interfertile. I found nothing authoritative that the pregnancy couldn't go full term in either case, though problems and issues wouldn't be surprising.
But it would be nice if we could once and for all dispense with the creationist argument of "a dog is a dog is a dog" by discovering that there actually are some breeds of dogs that are not interfertile.
You noted the main problem, that most people would be relucant to introduce this argument into a discussion: "A guy on the Internet told me that his vet told him that Great Danes and chihuahuas can't interbreed and are actually different species." And of course anybody convinced would have to say (if honest), "A guy on the Internet told me that another guy on the Internet told him that his vet told him..."
So speaking for myself, I have to remain skeptical and not use the information until I have a reliable reference.
--Percy