The demo squeeze page shown below uses the backstretch jQuery script to make the background image of the page mobile responsive. The image is not in fact a background image in CSS terms but is a foreground image that it placed in the background. And by virtue of being a foreground image it will resize according to the device. Very clever. So clever in fact that I incorporated into the Genesis Club Pro plugin to make it easier to use.
The Genesis Club Pro plugin makes it easy to set up this feature by adding a box to the Edit Page/Post admin page that allows you set up one or more background images and also change the opacity of the content on the page so you can see the background faintly behind the text.