They are two of the smartest men of their generation, both magna cum laude products of Harvard Law School, both cerebral and charming and ambitious. They vaulted to the highest offices in the land after just short stints at the next level down, and each was seen initially as a conciliator only to lead on the strength of his own majority.

Many years after their campus days in Cambridge, Mass., President Obama and Chief Justice John G. Roberts Jr. have emerged as the intellectual gladiators in a great struggle over the role of government in American society. In this moment of churning uncertainty and ideological ferment, it is a struggle that is already defining the selection of the next Supreme Court justice and could easily help shape the course of the nation for years to come.

Much more so than last year, when he made his first nomination to the court, Mr. Obama has Chief Justice Roberts on his mind as he mulls his second, according to Democrats close to the White House. For an activist president, the chief justice has emerged clearly in recent months as a potentially formidable obstacle, and Mr. Obama has signaled that he plans to use the political arena and his appointment power to counter the direction of the Roberts court.

“He’s very concerned about the activism of the court in recent terms,” said Senator Patrick J. Leahy of Vermont, chairman of the Judiciary Committee, ticking off a series of cases that angered liberals, most notably allowing corporations to spend freely in election campaigns. “He wants to make sure he puts somebody on there who is not going to take radical steps like that.”...