Mark,

That's going to be a very close one, but there might be a chance to get it through.

Geometrically speaking, for the purpose of this exercise your couch (if looking from a side) can be compared to a right-angled triangle. Let's assume you have enough space in front and behind the doorway, so that the couch will be pushed straight (no turns):

Having the sides of the triangle as 40" and 32" the height  is approximately 25", as shown on the image below. That would leave you with a combined 3" of space on both sides - pretty close.  

So, to answer your question, yes, theoretically it is possible to fit your couch in the doorway, but in practice it might be a bit harder if the doorway doesn't have enough space in front or behind it, or if the couch doesn't fit well in our triangle.