teijenkins found itself unable to complete an update because it was out of disk space. This was initially surprising, but I discovered that it was actually the small boot partition that was out of space, because of the accumulation of old kernels. This command:

dpkg -l 'linux-*' | sed '/^ii/!d;/'"$(uname -r | sed "s/\(.*\)-\([^0-9]\+\)/\1/")"'/d;s/^[^ ]* [^ ]* \([^ ]*\).*/\1/;/[0-9]/!d' | xargs sudo apt-get -y purge

cribbed from this page cleaned out the old kernels and solved the problem.