A larger influence will be Vice President Joe Biden, who in his former role as chairman of the Senate Judiciary Committee presided over several Supreme Court nomination fights. A member of the White House staff said that Biden's role would be "informal and ad hoc," but would include frequent consultation with the president, particularly on questions of strategy.
Ron Klain, Biden's chief of staff and a former clerk to Justice Byron R. White, also will be involved, the senior official said. Klain was chief counsel to the Senate Judiciary Committee during the tumultuous confirmation hearings of Justice Clarence Thomas.
Still, the center of power clearly will remain in the Oval Office. The president, who once taught constitutional law, signaled Friday that he personally would run the process along with Craig and other senior advisors.
Obama has sent mixed signals about what kind of jurist he would appoint, in contrast with George W. Bush, who as a presidential candidate left no question that he would choose conservatives in the mold of Antonin Scalia.
In a 2008 interview with the Detroit Free Press, Obama identified Marshall and other liberal icons of the court as "heroes of mine." But he added: "That doesn't necessarily mean that I think their judicial philosophy is appropriate for today."
At other times, Obama suggested that he was inclined to name moderates in the mold of President Clinton's choices of Ruth Bader Ginsburg and Stephen G. Breyer -- not known as bold advocates of liberal jurisprudence in the way Scalia is viewed on conservatism.
During Obama's U.S. Senate tenure, 2005 to 2008, the parties were locked in bitter partisan conflict over Bush's judicial nominees. Obama was one of 25 senators who supported a filibuster against the Supreme Court nomination of Samuel A. Alito Jr.
But he also has expressed reservations about the tactic.
In "The Audacity of Hope," his second memoir, Obama wrote that he had sympathy for the view that a president has the right to his own judicial nominees, and that Democrats should not try to win victories through parliamentary maneuvers such as filibusters.
"Elections ultimately meant something," he said he told a friend. "Instead of relying on Senate procedures, there was one way to ensure that judges on the bench reflected our values, and that was to win at the polls."