In public, White House officials continue to argue that Mr. Obama struck the right balance last December, and sent the right signals, when he called for a short-term troop increase followed by a drawdown. “America has no interest in fighting an endless war in Afghanistan,” he said then, quoting President Eisenhower about the importance of balancing America’s foreign commitments with its domestic needs.

But when granted anonymity, some senior White House officials who a few months ago said that this would be “the year of Kandahar”  referring to plans to retake control of the city that was the spiritual center of the Taliban  now acknowledge that the chances of progress there are growing more remote.

From the start of Mr. Obama’s review of the war’s strategy last year, he and his advisers debated the debilitating effects of what one called “the weariness factor.” Their calculation was that the withdrawal from Iraq, combined with the 18-month limit on the troop increase established by Mr. Obama, would quiet critics in his own party. That assessment proved optimistic. Earlier this month, 153 Democrats, including the speaker of the House, Nancy Pelosi, voted in favor of an amendment that would have required a clear timetable for withdrawal. Only 98 Democrats joined Republicans in defeating it.

But over the long term, what may be more damaging is the fact that members of the foreign policy establishment, even those who vigorously supported ousting the Taliban in 2001 after the 9/11 attacks, are gaining traction with arguments that the White House has simply failed to make the case that the rising cost is worth it.

“After nearly nine years of war,” Richard Haass, the president of the Council on Foreign Relations and a senior official in Mr. Bush’s State Department, wrote over the weekend in Newsweek, “continued or increased U.S. involvement in Afghanistan isn’t likely to yield lasting improvements that would be commensurate in any way with the investment of American blood and treasure. It is time to scale down our ambitions there and both reduce and redirect what we do.”

Mr. Haass is not recommending full withdrawal. Instead, he said in an interview, “I’m talking about reducing combat troops and operations and costs and casualties by more than half,” leaving mostly Special Forces, air power and trainers for Afghan troops in the region. In Kabul on Tuesday, President Karzai talked about having Afghan soldiers and the police taking responsibility for security by 2014. “Why should we be confident of that,” Mr. Haass asked, “given the history of Afghanistan?”