Countries don't have "friends" - they have "interests".
Putin and Obama may hate each others guts? But you can bet that both have their "interests" involved in this Syrian deal. They are not doing it because they are "friends".
I can't help but think that Obama is going against some very strong pro-war "interests"? They would prefer that he make the decisions all by himself, without Congress, and bomb the hell out of Syria so they can make more bombs and make more money. But Obama seems to be going against the grain, in my opinion.
He seems to be thinking of his legacy? He has mentioned constitutional reasons for taking the issue to Congress. This is not politics as usual, with Presidents making decisions about going to war all on their own. If he can pull this off in Syria, it will be a big part of his legacy. And he will piss off a lot of influential "interests".
However, the pro-war devils are whispering in his ear at all times. They have grown accustomed to having their way with the Presidents. They do not want him to go to the UN. They do not trust the UN. They do not want a peaceful resolution to the crisis. They would prefer another war.
Putin, on the other hand, is the ultimate pragmatist and realist. He believes Obama will carry thru with his threat to bomb Syria. He knows that Syria does not have the means to defend itself against the modern American weapons. Also, he knows that Assad has been weakened immensely by his war with the "rebels". He understands that Russia could lose one of its oldest allies in that part of the Middle East. It is in his "interest" to negotiate. If he can give up the chemical weapons but keep Assad in power and keep Syria intact, then it would be a victory for him. He is negotiating for survival of Syria as an ally of Russia.
Sun Tzu said, "Know your enemy and know yourself and you can fight a hundred battles without disaster."