Assuming that sticks, it's game. The White House just achieved its goal.
Remember: The White House's aim here wasn't to topple Assad, or even hurt him. It was to affirm and reinforce the international norm against chemical weapons. Here's how President Obama described it to NBC News:
The chemical weapons ban that has been in place is not something that only protects civilians. It also protects our own troops. You know, they don't have to wear gas masks even in tough battlefields because there is a strong prohibition and countries generally don't stockpile them. And if we see that ban unravel, it will create a more dangerous world for us and for our troops when they're in theater as well as for civilians around the world. It is worth preserving.
Assad is now agreeing to preserve and strengthen that norm. He's agreeing to sign the treaty banning chemical weapons -- a treaty Syria has been one of the lone holdouts against. He's creating a situation in which it would be almost impossible for him to use chemical weapons in the future, as doing so would break his promises to the global community, invite an immediate American response, and embarrass Russia.
This is, in many ways, a better outcome than the White House could have hoped for. Punishing Syria may or may not have actually reinforced the norm against chemical weapons -- particularly if the strikes went bad and the American people punished members of Congress who voted for them. But Syria joining the treaty against chemical weapons definitely, almost definitionally, reinforces the ban.
Now, there are obstacles between here and there. The White House wants to see this ratified in the UN Security Council and subject to tough international monitoring, and Russia says that means forswearing force against Syria. And there's always the chance that Assad's spokesman pops up tomorrow with a press release that says, simply, "syke!"
But the White House shouldn't work too hard to set the bar high here. If Assad is willing to sign the treaty and stop using chemical weapons, they should declare victory. It's a better outcome than they could have hoped for. And they might get it without firing a single shot.