What might that strategy be? Negotiated deals with different Taliban leaders that would splinter their followers.
But it's a peace path with potential potholes.
The idea gained traction this week after a reported truce between a Taliban group in Badghis Province and the Afghan government of President Hamid Karzai. (The main Taliban spokesman denied the deal.)
In addition, the British foreign secretary, David Miliband‚ gave a speech that laid out a strategy to "fragment the various elements of the insurgency, and turn those who can be reconciled to live within the Afghan constitution."
For both the United States and Britain, July has been the deadliest month for troop casualties since the 2001 US-led invasion ousted Al Qaeda and drove the Taliban from power. Leaders in both Western countries face new pressures to end their involvement in the conflict.
Not wanting to define the terms of a US "victory" in Afghanistan, Mr. Obama says the main goal is simply preventing Al Qaeda from operating there again. Many in the Taliban, who have had an uneasy relationship with Al Qaeda, may agree with him.
As Richard Holbrooke, Obama's chief envoy to the region, told the BBC: "There is room in Afghan society for all those fighting with the Taliban who renounce Al Qaeda and its extremist allies, who lay down their arms, and who participate in the political life of the country."
What is also helping drive the idea of making deals with the Taliban is the Aug. 20 election in Afghanistan for president and provincial council members. Large crowds are turning out for many of the 39 candidates. (President Karzai appears the favorite to win.)
Taliban leaders lack popularity among Afghans because of their ruthless rule during the 1990s. And despite their recent military successes against NATO troops, the election only showcases their political weakness. Many among the Taliban may be tempted to eventually join the democratic process in hopes of regaining power – in a similar way that Sunni insurgents did in Iraq, which caused that war to ebb in 2007.
In fact, it was Gen. David Petraeus, who now oversees US strategy in Afghanistan as regional commander, who initiated the strategy of negotiating with Iraq's Sunni tribal leaders. He sees opportunities for granting amnesty to Taliban fighters.
Such a strategy, however, is fraught with potential problems. Obama must be careful in how he pursues it.
The US, for instance, must let President Karzai take the lead in any negotiations, otherwise Washington may be seen as undercutting his legitimacy.
By sending in more US troops and beefing up civilian aid, Obama has given the Afghan government more leverage to strike pacts with local Taliban. But talking to the enemy isn't easy unless you first know what can and cannot be given away.
Obama may have little time to work out such deals before US opinion turns against the war. But both he and the leaders in Kabul need to tread carefully down this path of peace.