At a Brookings forum earlier this week former CIA man Bruce Riedel, who led the Obama White House's Afghanistan review earlier this year, put this spin on the stakes there:

The triumph of jihadism or the jihadism of Al Qaeda and the Taliban in driving NATO out of Afghanistan would resonate throughout the Islamic World.This would be a victory on par with the destruction of the Soviet Union in the 1990s. And, those moderates in the Islamic World who would say, no, we have to be moderate, we have to engage, would find themselves facing a real example. No, we just need to kill them, and we will drive them out. So I think the stakes are enormous.

This is not a rationale you often hear from the administration and its defenders, perhaps because it sounds eerily like one of the core Bush administration justifications for slogging it out in Iraq. But given the murkiness of other arguments for a prolonged engagement, I suspect this one carries more weight at the White House than people realize.