Copy PKZIP 19GB Video File to a 32GB Flash

Hello,

Please tell me if I can copy a PKZIP'ed video file that is 19GB on my hard drive to my newly purchased SanDisk 32GB Cruzer USB 2.0 Flash Drive. When I try it says "The disk in the destination drive is full. Insert a new disk to continue." If I retry, it says "There is not enough free disk space". The flash drive was purchased at Walmart and indicates it has free space of 29.8 GB. I also said I did not want to use U3 and just wanted to use the flash for storage only. I was able to copy multiple files that totalled 406MB, so I would know it would receive data. I deleted those files and tried again with the same result. Help, I am trying to reach a deadline to mail this file out by the end of the day via Fedex for my wife's Masters project.

Thanks