Unless you DD a rebuilt image, the installer needs a bit more than 128MB- however, the OS itself manages to barely fit into 64MB.

root@superteeny:/# free -h
              total        used        free      shared  buff/cache   available
Mem:            64M       35.2M          1M         48K         57M         25M
Swap:            0B          0B          0B
root@superteeny:/# cat /etc/debian_version 

It’s tight, but workable. It’ll work quite a bit better with swap (or RAM, really). I just did this to show that it is possible.

I also ran it with a manual upgrade from Wheezy on an OpenVZ container, and it worked swimmingly well. I wouldn’t suggest it, but it is possible.