It was not a theoretical question: Mr. Obama has placed himself at the helm of a top secret “nominations” process to designate terrorists for kill or capture, of which the capture part has become largely theoretical. He had vowed to align the fight against Al Qaeda with American values; the chart, introducing people whose deaths he might soon be asked to order, underscored just what a moral and legal conundrum this could be.

Mr. Obama is the liberal law professor who campaigned against the Iraq war and torture, and then insisted on approving every new name on an expanding “kill list,” poring over terrorist suspects’ biographies on what one official calls the macabre “baseball cards” of an unconventional war. When a rare opportunity for a drone strike at a top terrorist arises — but his family is with him — it is the president who has reserved to himself the final moral calculation…

They describe a paradoxical leader who shunned the legislative deal-making required to close the detention facility at Guantánamo Bay in Cuba, but approves lethal action without hand-wringing. While he was adamant about narrowing the fight and improving relations with the Muslim world, he has followed the metastasizing enemy into new and dangerous lands. When he applies his lawyering skills to counterterrorism, it is usually to enable, not constrain, his ferocious campaign against Al Qaeda — even when it comes to killing an American cleric in Yemen, a decision that Mr. Obama told colleagues was “an easy one.”…

But the strikes that have eviscerated Al Qaeda — just since April, there have been 14 in Yemen, and 6 in Pakistan — have also tested both men’s commitment to the principles they have repeatedly said are necessary to defeat the enemy in the long term. Drones have replaced Guantánamo as the recruiting tool of choice for militants; in his 2010 guilty plea, Faisal Shahzad, who had tried to set off a car bomb in Times Square, justified targeting civilians by telling the judge, “When the drones hit, they don’t see children.”

Dennis C. Blair, director of national intelligence until he was fired in May 2010, said that discussions inside the White House of long-term strategy against Al Qaeda were sidelined by the intense focus on strikes. “The steady refrain in the White House was, ‘This is the only game in town’ — reminded me of body counts in Vietnam,” said Mr. Blair, a retired admiral who began his Navy service during that war.