Failed apt-get upgrade on live USB

I could use some help. I've downloaded and installed Kali 1.05 to a USB, confirmed the SHA1SUM, installed using the standard dd if=iso of=/dev/sdb. I get a 2.35 GB "live" partition. I partitioned the unused space to a 14 GB "persistence" partition. I boot to the USB device; all comes up apparently fine. Running apt-get update then apt-get upgrade works until late in the upgrade process, when I get a "no space on device" error. I cannot increase the size of the partition, even booting into another Linux and working with gparted. It appears that one of the directories has maxed out its inodes and "space". I cannot find mention of this situation in the documentation, forums, via search engine. Ideas? Experience?