Resize Background Image for certain area in theme?

Hello!

I’m looking for some guidance on making this client’s website a bit more mobile friendly.

When you click on the link below, you’ll see the website URL at the top.

http://screencast.com/t/UB9ypuXrF232

On the home page, the whole area with the client’s photo is a big widget module. Behind the widget — which is a rotating block of text — is a background image of my client, his book, and a purchase button.

I know how to use CSS code to make the background fit the FULL WIDTH of the browser window. But, is there a way to make it ONLY the width of the website itself?

Any guidance would be wonderful! I’ve been struggling with this for weeks. AND, if you have suggestions for doing it completely differently — I’m open to them!

Thanks in advance,
Cynthia