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But the Bush administration’s shift toward war with Iraq left the Western powers without enough resources on the ground, so by 2006 the Taliban had regrouped into a serious military threat.

As a candidate, Mr. Obama promised to refocus America’s resources on Afghanistan. But by the time he sent 33,000 more troops to Afghanistan in December 2009, years of war in Iraq and Afghanistan had drained Western resources and sapped resolve to build a viable Afghan state.

And over time, his administration has grown weary of trying to tackle Afghanistan’s seemingly intractable problems of poverty and corruption. The American people have grown weary too.

While most Americans are sympathetic to the plight of the Afghan people, they have become deeply skeptical of President Hamid Karzai’s willingness to tackle corruption and political patronage and the coalition’s chances of “budging a medieval society” into the modern world, says Ann Marlowe, a visiting fellow at the Hudson Institute, a policy research organization in Washington.

“With millions of veterans home and talking with their families and friends some knowledge of just how hard this is has percolated down,” said Ms. Marlowe, who has traveled to Afghanistan many times.