President Barack Obama is backtracking on his warning that Britain would go to the “back of the queue” for a U.S. trade deal, as he tries to contain the fallout of the U.K.’s decision to leave the European Union. The shift in tone illustrates how Britain’s vote has abruptly scrambled Obama’s reality. Where the president had tried to encourage the U.K. not to rashly abandon the European bloc, he now must reassure Britain that its decision to do so won’t mean its demise. His priority of locking in trade deals before leaving office now becomes a distant second, behind the...