It would be very interesting to see what would happen if it doesn't receive Congressional approval. With the statement from Pelosi, it would put the administration in a position where they either have to back down, or openly defy the vote and take the risk. This entire situation is a political nightmare.
I kind of think that the two parties have an agreement: the bigwigs will act all gung-ho about it so they can get the international posturing they want, but the underlings are ordered to vote against it. The rank and file can just say their constituency doesn't agree with it. (Chances are, they don't, given that unlike what they were told about Iraq/Afghanistan, there's no tangible threat to the States). This way, they don't actually have to commit to anything militarily but they get to carry a big stick.