Explain fully what you are doing? Info on the LR version and about the Operating System you are using.
One possible explanation would be if the Publish collection you are trying to drag pictures into, is a Smart Published Folder / Smart Photoset / whatever - that is, one whose membership is defined by set criteria.
This kind of setup works the same way as a Smart Collection does. It is not possible to manually drag images into such a grouping. Any which have the qualifying attributes, will appear there automatically. Those which lack the qualifying attributes, do not appear there.
The problem has sorted itself, and I cannot explain why.
I consider myself to pretty good with Lightroom, but this one had me baffled. As, Richard pointed out, that the likely explanation would have been if I was in a smart collection etc. I wasn't I was in 'all photos'. I am using Wacom tablet with a mouse, and a ShuttlePRO. It could have been system error, i.e. to many devices.