Only nine months ago, the Pentagon pronounced itself reassured by the early steps of a new commander in chief. President Obama was moving slowly on an American withdrawal from Iraq, had retained former President George W. Bush’s defense secretary and, in a gesture much noticed, had executed his first military salute with crisp precision. But now, after nearly a month of deliberations by Mr. Obama over whether to send more American troops to Afghanistan, frustrations and anxiety are on the rise within the military. A number of active duty and retired senior officers say there is concern that the president...