I figured this out for my MacBook Pro. First, i hardwired my MBP and Apple TV with a standard Ethernet cable. Then I enabled Systems Preferences/Sharing/Internet, then indicated "From" as Airport and "To be shared with" as Ethernet. Then I turned on Airparrot and could mirror with ease. To go back to WiFi Apple TV, unplug.
But that solution doesn't work with my Air. I can't use standard Ethernet except with an Apple adapter, to fit into the USB port. (My Mac then wants to switch to USB Ethernet as source, but that's not right. Source remains Airport, ie, WiFi.) In System Preferences/Sharing, there's no Ethernet to be "shared with," only Ethernet Adapter (en) and that seems not to work. USB Ethernet doesn't work, either. This is a sticking point.
Any thoughts or ideas would be most welcome.