The poops will normally fall off on their own, or the budgie will preen themselves clean. If you try to pull it, it can yank at their sensitive little downy feathers and cause some pain. If you insist on getting the poops off, then you can use some warm water to help soften it enough for it to fall off.
Budgie droppings can be on the stiff side if they are not taking in any water. Giving them vegetables and high water content foods in addition to their regular water can help soften their droppings. I suspect budgies could get constipated....
What colour are the droppings? Normal ones can appear anywhere from dark brown to greenish when wet, and almost black to dark green when they are dry. How does the inner portion of the dropping look? (That is the urine portion). Is it sort of a creamy white? Or can you see it at all.
Here is a site that talks about budgie droppings; you may find it useful: