Going up and down stairs is very difficult for dogs and takes some practice for them. Very often the first few times end in a panic with feet slipping and legs being hurt.
Try to find a couple of steps outside to start with. Practice going up and down VERY slowly making sure the dog stops on each step. This should be pretty easy and gets the dog used to the idea of stairs mean slow. Once he can do six or seven with confidence tackle some inside stairs, not down to the basement. When these have been mastered you can move onto the basement stairs. Always do these excersises on the lead and very slowly. The dog is anxious and wants to get it over with as soon as possible so will rush, be prepared for this. As his confidence grows he will no longer feel the need to rush when on the lead. Once he is going down and up on the lead just hold the collar for th first couple of steps and let him go.
Terriers and the like are happy to go into small holes in the ground but it is not unreasonable for a dog to dislike the idea of going into a very large hole in the floor - he doesn't know what dug it and from the size of the hole, doesn't want to find out! By making a big deal of him going down there you are confirming his view of it as being different and possibly dangerous.