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!