Can I share my iMac's internet to iPhone or iPad over USB?

I have an iMac, connected to the Internet via Ethernet, and an iPhone 4. I would like to share the iMac's Internet connection to my iPhone via the USB Cable (because my wife dreams of a wifi-less household). I've set up Internet Sharing, specifying "sharing from: Ethernet via: USB IPhone", but when I test, the iPhone cannot connect to the Internet. Is there something I need to activate on the iPhone? iMac, mac os x version: Mountain Lion, 10.8.4 iPhone 4, IOS Version: 6.1