I've been thinking about this alot over the past couple of days even to the point that I began to investigate and play around with the Android SDK to see what I might be able to do, which is not alot at the moment.
I thought of this app functioning as follows:
1) We currently have a bunch of applications that allow the user to view and respond to their text messages through an interface on the browser or computer application using an app on the phone that "broadcasts" the messaging features of the phone out over either WiFi or bluetooth. (For example, the ones mentioned earlier in this thread.)
2) We also have something called "Remote Notifier" that sends out a "ping" when a new message is received to a listening service on a computer which notifies the user on the desktop.
3) If the existing functionality of those two are combined, we have an application that can put together a list of the messages on the phone (primary location), send it out to a secondary location (in this case a tablet), while also notifying the secondary location (tablet) of a new message received.
The app on the phone also gives the secondary location the ability to respond and edit the message list on the phone.
4) The second piece of the equation we would need is an app for the tablet, preferably optimized for the screen size in a 5manner similar to the way Gmail and the native email client handle messaging, (with a list of messages on the left, and the conversation view on the right) that allows the user to browse their messages on the phone and reply within the app.
If the app on the tablet could "look" to the phone as the service provider instead of the network, I could even see notifications being created from within that app and displayed on the tablet just as if it was actually receiving the texts itself.