Well, there are clearly behavioral traits other than the cute response that go into protecting human infants; if phenotypical cuteness was the only factor here, for example, there'd be little incentive to preferentially protect your own children. Parents that I've talked to have on occasion described their own kids as apocalyptically cute relative to pretty much anything else, but I'm pretty sure there are things other than phenotype involved here.
I don't think the evidence for a pedomorphic interpretation of cuteness is quite conclusive, but there do seem to be a serious dearth of competing hypotheses, and the evidence is certainly suggestive: the combination of small body size, a rounded body and head of large size relative to limbs, big eyes, soft features, playful behavior etc. all seem like they add up to a pretty good match. It also seems to be a culturally universal phenomenon, and those are quite rare.
Alicorn's point about cuteness giving us an unusual number of false positives relative to (say) sexiness is well taken, but I'm not sure how strong it actually is; superstimuli for sexiness that don't match real human phenotypes are definitely out there. Sexual selection's also under intense pressure relative to most other evolutionary cues, which might imply a need for our instincts in that area to be more accurate, although it seems (to my non-biologist self) like childrearing should be in the same ballpark.
Superstimuli for sexiness are like superstimuli for taste: take the reproductively best things in the ancestral environment, and exaggerate their characteristics outside of what was found there. For example, prominent sexual characteristics are sexy; Escher girls made mostly of breasts and buttocks are therefore sexier. Watanuki is such an example; the gangliness and androgyny are are but possible, the legs and facial structure are exaggerated but not that far from realistic equivalents.
Also, are many people sincerely attracted to Jessica Rabbit? It seems to me like she only represents sexiness, like we immediately understand a stick figure in a skirt to mean "woman".
Daniel Dennett has advanced the opinion that the evolutionary purpose of the cuteness response in humans is to make us respond positively to babies. This does seem plausible. Babies are pretty cute, after all. It's a tempting explanation.
Here is one of the cutest baby pictures I found on a Google search.
And this is a bunny.
Correct me if I'm wrong, but the bunny is about 75,119 times cuter than the baby.
Now, bunnies are not evolutionarily important for humans to like and want to nurture. In fact, bunnies are edible. By rights, my evolutionary response to the bunny should be "mmm, needs a sprig of rosemary and thirty minutes on a spit". But instead, that bunny - and not the baby or any other baby I've seen - strikes the epicenter of my cuteness response, and being more baby-like along any dimension would not improve the bunny. It would not look better bald. It would not be improved with little round humanlike ears. It would not be more precious with thumbs, easier to love if it had no tail, more adorable if it were enlarged to weigh about seven pounds.
If "awwww" is a response designed to make me love human babies and everything else that makes me go "awwww" is a mere side effect of that engineered reaction, it is drastically misaimed. Other responses for which we have similar evolutionary psychology explanations don't seem badly targeted in this way. If they miss their supposed objects at all, at least it's not in most people. (Furries, for instance, exist, but they're not a common variation on human sexual interest - the most generally applicable superstimuli for sexiness look like at-least-superficially healthy, mature humans with prominent human sexual characteristics.) We've invested enough energy into transforming our food landscape that we can happily eat virtual poison, but that's a departure from the ancestral environment - bunnies? All natural, every whisker.1
It is embarrassingly easy to come up with evolutionary psychology stories to explain little segments of data and have it sound good to a surface understanding of how evolution works. Why are babies cute? They have to be, so we'll take care of them. And then someone with a slightly better cause and effect understanding turns it right-side-up, as Dennett has, and then it sounds really clever. You can have this entire conversation without mentioning bunnies (or kittens or jerboas or any other adorable thing). But by excluding those items from a discussion that is, ostensibly, about cuteness, you do not have a hypothesis that actually fits all of the data - only the data that seems relevant to the answer that presents itself immediately.
Evo-psych explanations are tempting even when they're cheaply wrong, because the knowledge you need to construct ones that sound good to the educated is itself not cheap at all. You have to know lots of stuff about what "motivates" evolutionary changes, reject group selection, understand that the brain is just an organ, dispel the illusion of little XML tags attached to objects in the world calling them "cute" or "pretty" or anything else - but you also have to account for a decent proportion of the facts to not be steering completely left of reality.
Humans are frickin' complicated beasties. It's a hard, hard job to model us in a way that says anything useful without contradicting information we have about ourselves. But that's no excuse for abandoning the task. What causes the cuteness response? Why is that bunny so outrageously adorable? Why are babies, well, pretty cute? I don't know - but I'm pretty sure it's not the cheap reason, because evolution doesn't want me to nurture bunnies. Inasmuch as it wants me to react to bunnies, it wants me to eat them, or at least be motivated to keep them away from my salad fixings.
1It is possible that the bunny depicted is a domestic specimen, but it doesn't look like it to me. In any event, I chose it for being a really great example; there are many decidedly wild animals that are also cuter than cute human babies.