The strategy of Petraeus, implemented originally by McChrystal, is a perfectly valid approach, probably the only real workable COIN strategy since in modern times it is unacceptable to just depopulate and lay waste to a rebellious countryside (Also a proven successful COIN strategy, historically).
What he's doing has been proven by other players than us in the past, it is not some untested flash in the pan. That said, it DOES take many years of enforced stability for it to take root, what's called in military jargon 'The Long War' vs. the kind of war Gulf I or Kosovo was. Thing is, it works much faster in countries that have more developed economies and more visible-to-the-people economic benefit from a stable central government.
Afghanistan is more or less a 'Worst case' COIN war, well except for lacking jungles, that's about all that would make it worse yet. The enemy has all the classic preconditions for successful guerrilla war set up in his favor, to include a willingness to take extremely unfavorable loss ratio ass-beatings until we get tired of losing even the small end of those numbers and sanctuary across the border.
In other words our COIN strategy bears fruit a whole lot quicker in a place like Iraq than in a place like Afghanistan. Iraq is a place where the vast majority of the population sees a better life in peace than in continued warfare, there's a tangible difference between the two conditions to them. In comparative terms, let's say it's like Yugoslavia was - civilized, even mildly industrialized, literate and aware of the wider world and wanting to be involved in it, but riven by factional fighting. Afghanistan is more like the kind of African colonial state as depicted in 'Heart of Darkness' - a thin veneer of civilization, mostly imported and misspent, but with a backward population ruled by warlords who regard conflict as actually providing more opportunities for themselves than peace (Peace after all means not being able to hijack convoys, or raid your competition's villages), where loyalty is strictly local and the central government is generally regarded as an unnecessary annoyance and an irritating hindrance to your life goals of increased power and personal enrichment.
The strategy will work in Afghanistan only if we have the political will to pursue it to its logical consequences, which I frankly doubt, since it will mean maintaining serious credible forces to backstop the central government for at least two decades, and a substantial reaction and training force well beyond that. In other words we would have to stay there in force until Western expectations fo fair government and straight dealing are enforced long enough for a couple of generations to grow up under them and think of them as the norm.
If we actually follow Obama's timetable, or even a stretch version of it, our departure will signal a replay of the Soviet pullout, with the central government eventually going Tango Uniform. That timetable is entirely in the hands of the aAdministration, not the generals, of course. People forget that the Soviets too had mcuh more than a military presence, but did their best to bring the Afghans up to the Soviet version of a modern outlook and values. From the overthrow of the king, in which they were heavily involved, they had over ten years at it, and they did indeed convince a lot of the same sub-populations with whom we have made some headway. It wasn't enough to survive their departure, when they pulled out it was like clock was suddenly dialed back a hundred or two years.
Oh, and yes, Steele's an idiot, he needs to go.