The White House could argue that no such outcome was possible until the U.S. threatened to use force. With the U.S. threatening to use force, that provided the kind of leverage that had been missing. Faced with the possible threat and perhaps concluding that the outcome could cause it to lose its battlefield advantage (air power and missile systems), the regime decided to trade off its chemical weapons to minimize the damage to its battlefield prospects. Thus, the U.S. goal of eliminating chemical weapons use in Syria was achieved.
That the U.S. tactics were remarkably sloppy, that the President had essentially created his own dilemma with his "red line" that ran beyond international norms, and that the rebels would likely still possess some unknown quantities of chemical weapons would be largely irrelevant. The White House would focus on the goal that was achieved and it would be sufficiently large that it would be viewed as a success. Of course, the White House's messaging could be poor, as it has been on numerous Mideast issues, so its public relations effort could fall flat.
For now, it's too soon to know whether the Russian initiative will succeed. Much work will be required and full implementation will almost certainly take more than a week. Will the U.S. have patience? Will there be a set time beyond which the U.S. would conclude whether or not the framework had a good chance of success? There are many uncertainties.