I wouldn't make a sprite for background images, that's a world of pain. Why not just define a large background image via CSS, set it as static, vertical align to top, horizontally align to centre and allow it to clip past the window border? Then when a user resizes their browser window you'll always see the key parts of the image.
You'll have to remember the various 'important' resolutions to design at, and work around that. If you start slicing and moving in proportion with screen width, you're going to have a massive amount of Javascript and CSS work for the browser to do even before the page has rendered.
If you really want to make a 'stretchy' design, DIVs with percentage alignments are the way to go. Some advanced usage of CSS @media types will probably come in useful too so you can load a different set of image slices and have them move by different amounts depending on the initial resolution of the device; this is Responsive Design.