Can I restore/backup my iPhone 3GS with an iPhone 4s backup?

Long story short, my iPhone 4s is not working and I have a very recent backup of it. I'd like to restore that backup to my temporary iPhone 3GS. Is that possible? If so, how?

Added (1). My iPhone 4s was running the new 7 iOS when I backed it up and my iPhone 3GS can only run the latest 6 iOS. Is that the issue?

As long as they are on the same iOS version yes.

Yes, of course. First backup the info in your iPhone 4s to your iTunes, and than you could transfer them to your iPhone 3GS