It strikes me that Obama is playing a very smart game with his decision to ask Congress for the authorisation to act against Syria. If he can get the backing of a Republican-controlled Congress, he can play the “America is unified” card.
That makes his position much stronger with other countries. He will have not only (as he sees it ) a moral mandate, but also a democratic one. And where David Cameron lost because the people's representatives weren't behind him, Obama would have that backing.
And if he loses? To my mind, he's in something of a no-lose situation. If he loses the vote, he can simply blame the Republicans.