Actually, they can go "all-digital" at any time: The regulation provides them two options... either leave analog running, or provide (perhaps for a fee) a converter box that has analog video outputs. They have to offer one or the other until at least 2012 (when presumably they can make everything digital and stop offering converter boxes with analog outputs).
Having said that, in most areas, they're going to leave the local broadcast channels in analog for the duration. They may require you to have a box on every television for cable channels, though. However, that change-over, if it happens, has nothing to do with the broadcast DTV transition on June 12.