I've made a fix for this issue that should make its way unto the next beta patch. In the mean time however, there is a workaround that might get you up and running.
Quit the game first, then look under your My Documents/Starcraft II Beta folder, you should find a Variables.txt file there. You can open this file with your favorite text editor such as Notepad, and add the following line:
frameratecap=60
This will cap your framerate to 60 in the game, which should give your videocard some breathing room. You can put any number, see if a lower number like 30 helps as well, though you will lose framerate.
This is only a temporary workaround, an upcoming patch will have an automatic solution for everyone.