President Obama called Harry Reid, the Senate majority leader, to broach a particularly delicate subject. It was during last year’s government shutdown and standoff with Republicans, but Mr. Obama’s frustration focused on one of their own. The president said he suspected David Krone, Mr. Reid’s intensely loyal and influential top aide, of leaking to the news media, and requested that he stay away from future meetings. It did not take much time for the president’s comments to reach Mr. Reid’s right-hand man. To Mr. Obama’s surprise, Mr. Krone was listening in on the call. Suddenly, the aide piped up and...