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On the afternoon he held the eighth meeting of his Afghanistan review, President Obama arrived in the White House Situation Room ruminating about war. He had come from Arlington National Cemetery, where he had wandered among the chalky white tombstones of those who had fallen in the rugged mountains of Central Asia.

How much their sacrifice weighed on him that Veterans Day last month, he did not say. But his advisers say he was haunted by the human toll as he wrestled with what to do about the eight-year-old war. Just a month earlier, he had mentioned to them his visits to wounded soldiers at the Army hospital in Washington. “I don’t want to be going to Walter Reed for another eight years,” he said then.

The economic cost was troubling him as well after he received...