I had the same problem, but I found a workaround. See bug #873409. Somehow, the extraction step of some packages fails and dpkg gives a 'disk full' error, even though there's plenty of space. When I installed the package manually and gave the -D10 flag to dpkg, it worked. -D10 is just supposed to give more debug information, so this looks like a bug in dpkg.
Workaround:
When the installer fails: log in to a console from the installer environment.
chroot /target bash
apt-get -f install
Note which package failed to install
cd /media/cdrom/pool/main/<location of failing package>
dpkg -i -D10 failing_package.deb 2>/dev/null
apt-get -f install
exit
Hopefully apt-get now succeeds. Continue the installation procedure.
Be sure to exit the chroot shell, otherwise it might interfere with the installer because the target disk can't be unmounted.
Note that in my case the failing package was /media/cdrom/pool/main/l/linux/linux-headers-3.0.0-12_3.0.0-12.20_all.deb, which is part of the 'install the base system' installer step, so I had to retry that one first. Even though the error occured while installing the base system, the installer only showed it when trying to install the rest of the system.