You need to clarify a bit more. It all depends on your current configuration and the resolutions of your monitor and HDTV (screen size does not matter).
If your GPU were plugged into both a monitor and HDTV and used at the same time, then yes, it would put more stress on the GPU (but it is designed to handle that).
If you were to connect your GPU only to your HDTV and the HDTV has a higher resolution than your monitor, then yes, it would put more stress on the GPU. If the HDTV and the monitor have the same resolution, then it wouldn't cause any more stress than the GPU already experiences when connected to the monitor.