How to invert text color with respect to background in Illustrator?

Set the Blend Mode of your text items to Difference in the Transparency palette. Change the text color to white. You’ll probably notice the white doesn’t change to black in the “white” space. That’s because it’s actually not white, but transparent instead (Ctrl+Shift+D makes this easy to see). If you add a white background behind the white text, it will change to black again.

This will work even if the text has been rasterized into an image.

EDIT: Sorry, I did not realize the above only works in an RGB Document. To do the same thing in a CMYK Document, it’s a little different. Change the black background to white & Difference, then move it in front of the text.