Who's Afraid of Virginia Woolf?
Since there is room for debate as to who the protagonist is, it's probably no surprise that the role of antagonist is debatable as well. The antagonist is defined as the character that opposes the protagonist. Martha drives the action of the first two acts, making some believe that she is protagonist. If you choose to look at the play this way, George is definitely the antagonist, because he's the one who doing battle with Martha.
On the other hand, most scholars seem to think George is the protagonist, because he performs the final action of "killing" the imaginary son. In that case Martha is a daunting antagonist, who our hero, George, finally defeats in the end. No matter which label you use, it's clear that the action of the play is driven by the endless battles of George and Martha.