Logically and legally impossible. You can't "remove" someone from an office they do not hold (and have never held.) That point is beyond any further argument.
The only point to be argued is whether Obama is POTUS. If he is, then he could be removed for whatever reason pleases Congress. Otherwise, it is an outright impossibility.
I cannot imagine any possible SCOTUS ruling having to do with his being (or not being) a "natural born citizen" that would a) find that Obama is POTUS, and b) displease the Congress enough to impeach him. So either he is POTUS and will so remain until his term expires, or he is not POTUS, and the potential future SCOTUS ruling to that effect will require no further action by Congress (other than dealing with the matter of who will be POTUS.)
You can remove anyone from anywhere technically.
You cannot impeach a man who has no right to hold an office, you simply remove him, thru the courts if necessary.