I am doing something similar and I don't have this performance issue, so I don't think NGUI is the source of the problem. My money is on two possibilities: either you have a broader performance problem that is just showing up because of drag and drop, or the object you are trying to drag is REALLY complex.
To check for the first problem, I would learn how to use the Unity profiler pane.
To investigate the second, look for the panel that owns the dragged object -- this will be the first gameobject you encounter that is a direct parent of your dragged object that has a UIPanel component. Open up the draw calls window for that panel, then run your game. If you are getting a massive number of draw calls (e.g. in the hundreds), that's likely your problem.