Actually, the Twitterverse is saying the rest of congress is likely to vote, "No." Even if they're just doing it to disagree with Obama as usual, it's the right choice IMO.
Even Sen. McCain sounded like he was hedging when he said no specifics had been agreed on. I feel like that's District-talk for "we vehemently disagree but can't say that." Obviously the President would be happy to see Congressional approval, but even if they don't give him that, he should be glad. He has Peloisi saying approval isn't necessary, but at the same time, he could say that he respects the wishes of the American people as conferred to him through Congress and semi-gracefully back down from the proposal. That, of course, would put France, Turkey, the UAE et al. in an awkward position - they'd have pledged support for an offensive that no longer has a keystone leader!
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.