The first time President Obama sat down to pick a new Supreme Court justice, surprised aides discovered that he had gone beyond the briefing memos to read the leading candidate’s past judicial rulings. The president, a onetime constitutional law teacher, was in his element, a “legal nerd,” as one aide called him, putting theory into practice.

But if nothing else, the last seven years have made clear to Mr. Obama that the Supreme Court is anything but a nerdy, academic exercise. His current standoff with the Senate over replacing Justice Antonin Scalia culminates a profoundly consequential struggle over not just the law, but power, politics and his legacy.

During his two terms in the White House, the Supreme Court has given Mr. Obama fits, given him reprieves and now given him a new mission for his final year in office. He has publicly feuded with the court as few of his modern predecessors have. By one measure, he has enjoyed less success before the court than any president since World War II. But today his unexpected chance to remake the court depends on overcoming the formidable will of Senate Republicans.