No it isn't normal.
In a proper nest this should not happen, there should be enough hay to absorb liquids and fur to keep them warm. There should not be much poop.
How does the nest look like? Is it ok, dry hay (replace soiled stuff - I've heard of does that use the nestbox as toilet) and the kits are warm and nicely covered in fur? Are their bellies full?
It is necessary that they have a warm nest, if they are cold their digestion doesn't work properly. keep them warm and dry. If something is wrong with the nest, fix it, if the doe does something with the nest she shouldn't, remove the nest and put it back in twice a day for feeding. Same if weather and circumstances get the nest cold or wet.
Another issue that would effect the whole litter would be Mastitis,infected mammary glands and the milk gets contaminated. Check the doe, are her nipples red, swollen? Google for symptoms, I have no personal experience with that. It's not always visible, if it's that there are not many options, getting the doe treated by a vet asap and hope that the kits pull through, or handfeeding the kits. My hopes for already struggling kits wouldn't be very high.
There sure could be other reasons, but that is what I can think of right now.
Good luck.