Still got a problem when the user resizes the window, but it's an alternative. Another problem is the rather big number of different resolutions the visitors might be using. Looks fine in say 800*600 or 1024*768, but anything more than that and it's f*cked up.
Overall, I do not recommend using a largeish pic as a background. There's so much fluff on websites nowadays. Many aren't scaling very well, and it doesn't matter if you have a 10Mbit line if the webserver can't deliver.
If possible, the image should either be broken up into bits (such as top, left, right, bottom like if you want a frame around something), or be created so that it can blend in with either a background colour, or another (repeating) background image.
If you *really* want to make sure the site looks the same for everyone, ya gotta set a fixed size. And use DOM standards. No, wait, IE doesn't care much about that. Use both IE and DOM standards. No, wait, IE on Mac doesn't meet IE PC standards.
Let's see....
Firefox good. Rest bad. Apache good. IIS bad.