Was wondering if there is an application that can draw your desktop in one resolution and output from your graphics card in another? HDTV will only support 1024*768 natively
OS X does that, just put it into extended desktop mode. If you want to watch something on the external display, in most cases, draging the window to the other screen will make that the screen it will become full screen on.
Also, HD is 1280 x 720 and 1920 x 1080, although many screens are 1366 x 768.