Set one background to stretch across multi-monitor display?

Set your wallpaper to Tile. If the background is sufficiently large enough, it will stretch across the monitors. If it isn't, it will start repeating at the ends. You can use an image editing program to adjust the resolution or add whitespace to get it to work perfectly.

You can also use this trick to get different wallpapers on each monitor.

Display Fusion should do the trick.

http://www.displayfusion.com/

There are two versions, a free and a pro version. What you are looking to do only needs the free version.