Under normal circumstances, if a dog goes longer than 48 hours without defecating then there could be something seriously wrong going on.
Things that would cause a dog to be unable to defecate would be:
Constipation...often giving the dog some canned dog food (which is higher in liquid) and some canned pumpkin (only real pumpkin, not pumpkin pie filling) as a fiber addition will get things moving in the right direction.
Ingestion of a foreign body...if your dog has had any rawhides, bones, or if he eats non-food items such as socks, toys, towels, ect..then your dog should be seen by an emergency vet tonight for an x-ray to find where the blockage may be.
Recent diarrhea....if a dog has had several bouts of diarrhea in a short amount of time, it may take a day or two for them to defecate normally again. This is because the colon is empty, and it won't be refilled until the dog eats several times, and digests the food.
If your dog seems painful in the abdomen, has been attempting to defecate of vomit with no success, or seems lethargic, then you need to have him seen immediately by an emergency vet.
I hope this helps.
If you're positive that she hasn't defecated at doggy day care...then I'd start with giving her some canned pumpkin (squash will do the same thing, actually). A couple tablespoons should get things moving along.
It will simply make things a bit looser, due to the fiber.
There are no other side effects since it's simply pumpkin.