Your question doesn't tell us for which application you need this effect - a rendered animation I guess. (Or a game?)
If you don't need it to be live input, you can just do the following:
Set your camera to the desired position. For every frame the camera is 'active' as the portal is deployed, you have to be in camera view.
Now, just render the animation in this time period (as png's).
Next, go into photoshop/gimp/whatever, and put the portal on it like a border. Everything outside it should be alpha. (To achieve an animated portal you should use different portal borders, a static portal looks quite boring...)
Finally, back in blender, add a plane the size of your portal (you can also use the add-on "images as planes") at the place you want to let the portal appear.
Animating the Texture:
As this is complicated to explain just take a look at this video, which explains the process in detail.
If what I said wasn't visual enough, I could help out with sceenshots and a blend file.