What would the puppies look like? Let’s assume that artificial insemination is used… since mating the “natural way” isn’t likely to be successful.
:: obligatory smartass answer:: A dirty look from the chihuahua.
Birthing the natural way also isn’t likely to be successful, if it’s a Chihuaha bitch giving birth to half-Great Dane puppies. There could even be problems surviging in uetero.
But the actual insemination should be possible, and fertile. All dog breeds are the same species, and can inter-breed.
If you search the SDMB, you’ll see that people ask this question often. Basically, you can’t. Even though all dogs are genetically compatible, it won’t happen because their size makes their genitals incompatible, and no one is going to risk a purebred animal, or a favorite pet on a “this would be so kool” artificial insemination. You could breed them to intermediate sized dogs, then breed those intermediates, breeding out the intermediate traits, to produce a specific new variety you can breed amoung themselves, and try to register it as a new breed. But nobody’s going to do this sort of work just for their curiosity.
The video shows two dogs: a great dane and a chihuahua mix. It’s not both mixed into one dog, like the OP wanted.
Actually, that’s usually the status quo for french bulldogs:
Birth and reproductionFrench bulldogs frequently require caesarean section to give birth, with over 80% of litters delivered this way.[1] [2] As well, many French bulldog stud dogs are incapable of naturally breeding. This is because French Bulldogs have very slim hips, making the male unable to mount the female to reproduce naturally. Typically, breeders must undertake artificial insemination of female dogs.
That’s a video of a chihuahua mix and a great dane. Two dogs.
So a Great Dane bitch can’t get it doggy style from a Chihuahua?
Well, what do you know - size DOES matter.
I don’t see what the problem would be with birthing healthy puppies, as long as the large dog was the female.
But why would anyone want a 100lb Chihuahua? (And you though Dobermans were mean.) 
Actually, it’s not so much the genitals that are incompatible, as the developing fetuses with size characteristics from the larger dog would be too large inside the smaller dog. Reverse that and it should work without problem.
Did you hear about the male Chihuahua that mated with a female Great Dane?
.
.
.
Someone put him up to it.
Female Great Dane artificially inseminated with male Chihuahua? Well you could extrapolate from the experience with other “hybrid dogs” such as the Golden Doodle and Labradoodle - could be any combination of features and sizes in the same litter.
One cup.
I remember this from an issue of the Fabulous Furry Freak Brothers. It involved a step-stool and produced a dog called a “Great Wawa” with a huge body and a tiny little head.
Shouldn’t that be “Golden Retroodle”? 
For the win.
I kept kidding Mrs. Cad that I was going to take her dachshund male and akita female to breed dachitas (or dakitas). I believe the phrase she used was that it “would be an affront to God.” and she’s not even religious.
But who wouldn’t want a little miniature akita or a large 80lbs dachshund?