I don't know but it's working now... The .CR2 files (RAW files I found out) are being imported after I changed the destination directory. I didn't like the where I had them going before as a destination. Drive space isn't an issue either... So I don't know.
I have just got LR4 and the same thing happened to me after I chose a new directory to import them to, just refused to import them. I am importing Canon 5D2 CR2 raw files. However, when I used the default 'my pictures' it worked. Not good when you want to specify a folder for your images. Have you had any more insights into this?
I haven't had the problem occur since the original post of this thread. So, I'm not sure what happened exactly. I just changed the import directory and it worked.
Make sure you have permissions to write to the selected directory.