At that point, the U.S. could hand the problem back off to others and bring its troops home.
This last part is very important. The U.S. has been in Afghanistan for nearly nine years now, and it cannot afford to sustain large forces there indefinitely. The U.S. has a severe manpower and financial deficit, and every year that its forces are tied down in a strategically-insignificant country like Afghanistan is a year that the U.S. is unprepared for crises elsewhere. Don't imagine it's a coincidence that North Korea brazenly sunk a South Korean warship or that Iran marches ever-onward towards a nuclear weapon as America is tied down in two wars. Afghanistan, like Iraq before it, constrains U.S. ability to take military action elsewhere.
This is one reason that Obama felt the need to impose a timeline on operations in Afghanistan, suggesting that a "transition" of some sort would occur in July 2011. This is surprisingly soon, given that the surge of forces has not, even as I write, completely arrived in the country yet. But this also speaks to the manpower deficit I spoke of earlier; it takes time to cycle a limited number of forces into the country. It's also clear that there are political factors at work, as some Democrats and much of the liberal base has decided that Afghanistan is no longer "the necessary war" but just another war of choice after all,