Gil I think there are a couple of basics you need to come to grips with.
Assuming your Aperture library is on your start up disk and that you only have 13GB free, DO NOT PLACE ANYTHING ELSE ON THIS DRIVE, until you clear out some space adding more files to this drive is only asking for trouble.
100GB is represented by 9.9GB, yes, Aperture has created previews of the referenced files and has a database to describe them = 9.9GB, 100GB of master files/images still reside on the other drive though.
The folder of files you are trying to import, 19.4 GB, you say you are now using a managed file workflow, that being the case Aperture now copies the files into the library, so there is no way that 19.4GB will fit into 13.3GB, plus there will then be an additional 1-2GB, based on 110GB=9GB, of space required by Aperture.
I hope this makes sense.
Moving forward, get youself two external drives, have you library, managed or not, along with any referenced files on one drive, the other drive use for your back up.
Thanks for the feedback. Maybe I wasn't very clear, but I wanted to import the files as Referenced images, so the Aperture library shouldn't have increased more than the 2GB you mention. I managed to get my import done by starting a new library on the external drive where the (19.4 GB) image folder resides. I then merged that library into my existing library on my startup disk. Problem solved! I still don't know why the problem existed in the first place.
You are right about my need for more storage. I also need a new computer. My iMac is starting to groan under Aperture 3 and 20 MB NEF files from my D7000.
This must be a bug. Because I have the same issue when trying to import from my NAS to the Aperture Library on my local startup disk as referenced files.
It worked when I moved the Apertury Library to my second disk with enough free space. I guess when calculating the needed space for the import, Aperture doesn't respect the setting to keep images at the current location (i.e. as referenced files).