Does OS X have a setting that will let me apply a Gaussian Blur to the monitor or a specific window?
Warning: this is a workaround.

Terminal.app lets you set the exact settings of its window. If you set them correctly, you can get a transparent window with a gaussian blur. If you simply leave a window open in the background in Terminal while doing your work, then bring up Terminal when you want to, this should work great. You can even make the text transparent if you want.