When the Debian install asks you what device to use, give it /dev/sda or /dev/vda. For some reason /dev/cdrom wasn't working for me either. I ended up switching the ISO's device to virtio and tried /dev/vda and it worked.

The ISO was on /dev/vda and the target disk image was on /dev/vdb. Just make sure you install the bootloader on the disk image. Then when I removed the ISO, everything was just fine.