You cannot currently size a background image at a percentage, say 100% so that it would fit any browser width.
However I believe this is implemented in CSS3, but forget about that for now because it's ages away, plus it would cause problems with image re-sizing.
Your options are to have the background image, as a simple image e.g <img src="blah.jpg" /> and set that to 100% width and position it in a way to act as a background, but this implements extra markup and is not very good design.
Another option is to create the image so that it fades out towards the left and right into a common colour, and make it the size for the biggest resolution. That way small monitors get a nice background and large monitors also. The fading isn't needed but may help.
Check this site for example: http://www.webdesignerwall.com/
Their background image is huge, but on a small 1024x768 monitor you still get a nice looking background that doesn't seem chopped, whilst even bigger monitors are getting even more.