True constipation from internal problems is not common. The most common interference with Pooping comes from dried poop stuck in the hair around the anus and even a clump the size of a match head is enough to cause problems.
For safety check to make sure there is no dried poop in the hair around the anus as this can cause the puppy to delay defecation because it is uncomfortable. If there is dried poop in this area you can gently bathe it away with warm water and a little mild dish soap or if you have a small hair trimmer you can clip it out. Using scissors for this should be avoided as it is very easy to injure your puppy.