Comment 11 for bug 1134492

Downgrading is trivial: apt-get install xserver-xorg-lts-precise libgl1-mesa-{dri,glx}:i386

This is unsupported for newer hardware, because they're not tested with the older linux/xserver, but in your case it would work. It seems some interaction with multiarch is making it fail. Multiarch was already failing to switch correctly, causing the 32-bits libs to be uninstalled. If I install enough 32-bits applications I can make it uninstall kubuntu-desktop too.

But the failure the other way around is easier to test:

pbuilder-dist precise amd64 login
apt-get install --install-recommends ia32-libs xserver-xorg-lts-precise
apt-get install --install-recommends xserver-xorg-lts-quantal

Notice that ia32-libs gets removed by installing xserver-xorg-lts-quantal. However if I install ia32-libs afterwards it works, because that case was fixed in #1130419:
pbuilder-dist precise amd64 login
apt-get install --install-recommends xserver-xorg-lts-quantal
apt-get install --install-recommends ia32-libs

It's still easy to make the resolver die completely, too:

pbuilder-dist precise amd64 login
apt-get install --install-recommends xserver-xorg-lts-precise
apt-get install --install-recommends xserver-xorg-lts-quantal ia32-libs

if you add libgl1-mesa-{glx,dri}-lts-quantal:i386 to the last line, it will find the correct solution.