If all the files you're working with are on the same drive - project files and the ones you're trying to import - backup that entire drive immediately. If it says it's full and it's not, there's a problem with the Directory or the Volume Information Blocks. You are headed for serious data loss - complete and total.
However, if you're importing from another drive, it's possible the problem lies there.
But in the absence of more diagnosis data, I'm betting that it's your System drive, and that you are recording to it, too. Right? If possible do a complete backup immediately (hopefully the backup won't fail due to bad Directory), then reformat the drive and reinstall the Operating system and apps. Keep a close eye on it, there may be a hardware problem with that drive, and it's on it's way out. If there's a second drive involved, check that one thoroughly, too. At least run Disk Utility on all involved drives! But back 'em up first!
And I suggest you get an external drive and record audio to that. It's not impossible to record to your System drive, but you'll get much better performance, and way better *reliability* if you keep your Audio and System drives separate.