The Gnome 3.8 desktop is planning to ship without the fallback desktop that allows the Gnome desktop to function on computers that do not have the minimum specifications required to use the Gnome 3 desktop. But obviously you can use either the Lxde or Xfce desktops if your machine does not match the specifications required by the Gnome 3 desktop on Linux Mint and Ubuntu. But just type sudo apt-get install xubuntu-desktop or sudo apt-get install lubuntu-desktop and install two superior desktops that will be lighter on system resources than the Gnome 3 desktop is at the moment. I actually prefer using the Unity desktop on Ubuntu and the MATE desktop on Linux Mint. So if the Gnome desktop will no longer work on your machine just install another desktop that will be lighter on resources than that bloated desktop is at the moment. The Xfce desktop has been around for quite a while and is always a good choice if you want a Gnome 2.32 look-alike desktop that is very fast and reliable instead of Gnome 3. RIP Gnome 2.32.2.
Here is a look at the Debian 6.0 Gnome 2.32.2 desktop; this is Gnome when it was good: http://youtu.be/qo38vnYI8ek?hd=1&t=4m43s.