I really hope there's a good IronChariots article that addresses this, but not finding one I'm putting this here.
I'm not asking the question. Recently I've seen a number of good youtube atheists made awkward by arguments beginning along the lines of asking "Is it possible for a God to exist?". I believe this to be an excellent (from the apologists point of view) trick question. I saw several examples of an atheist responding with a very hesitant, guarded yes, and then I could not bear to watch the video go much further down hill from there.
This excellently takes advantage of atheists open-mindedness and avoidance of dogma. But ask yourself this, would you (or any other atheist) have responded yes if the question was "Is it possible for a married bachelor to exist?" We're overthinking the question if we're not responding with a flat no, for multiple reasons.
First of all, the asker always means his God. The asker will never be proposing some interesting philisophical concept worth any pondering, at least not in this way and not in a situation where this arguement is being proposed. Not only can you guess that the asker is a more conservative Christian, but likely also a creationist. Remember, the asker is really asking you if it's possible for HIS God to exist, and the most appropriate immediate answer is not only No, but that even bothering with the question is downright silly.
I suppose we fear the "Aha!" accusation that we're just dismissing God without consideration, but this question is sidestepping the consideration all together and jumping straight to your conclusion. My atheism is not without consideration. My atheism is the result of education and much consideration, and my immediate and automatic negative response to a question about the possible existence of gods is the conclusion of the debate, and no more dogmatic than my conclusion about the possible existence of married bachelors.
So, is it possible for a God to exist?
Is it possible for you to be wrong?
It is possible for me to be insane, disconnected from reality without knowing it. For the reality I have access to, it is not possible for me to be wrong.