By Jess Bravin

With the incoming leadership of the executive and legislative branches nearly a carbon copy of the current versions, Tuesday’s election could have the biggest effect on the sole unelected branch of government: the federal judiciary.

President Barack Obama will need help from the Republican-controlled House to enact legislation, but he needs only the Senate, where Democrats strengthened their majority, to approve judicial nominations. Should vacancies arise on the narrowly divided Supreme Court, Mr. Obama, who appointed two justices during his first term, could leave a lasting imprint on constitutional law.

No current justice has indicated a desire to surrender his or her lifetime post. But with four justices older than 70 and eligible to retire at full salary, a single departure could buttress the court’s liberal wing—or end the tenuous conservative majority that Republicans have labored to build since the Nixon administration.

One name increasingly mentioned in liberal circles is Judge Paul Watford, 45 years old, who was confirmed earlier this year to the Ninth U.S. Circuit Court of Appeals in San Francisco. Judge Watford is a former federal prosecutor and corporate lawyer who clerked both for Judge Alex Kozinski of the Ninth Circuit, a Reagan appointee, and Justice Ruth Bader Ginsburg, who at 79 is the eldest member of the Supreme Court.

If the president wants “someone young with U.S. Court of Appeals experience who has the traditional indicia of being a brilliant legal mind, the name that stands out is Paul Watford,” said Ian Millhiser of the Center for American Progress, a left-leaning think tank. If appointed, Mr. Watford would become the third African-American, after the late Thurgood Marshall and Justice Clarence Thomas, to sit on the Supreme Court.

Many believe, however, that if Justice Ginsburg retires, Mr. Obama is likely to seek a female successor. In that case, one name being mentioned is Ninth Circuit Judge Mary Murguia, whom the president elevated from the federal district court in Arizona. Judge Murguia, a daughter of Mexican immigrants, attended the University of Kansas and served as a federal prosecutor in Arizona under then-U.S. Attorney Janet Napolitano, now secretary of homeland security.

The relative paucity of liberal stars on the federal bench makes it likely that Mr. Obama will consider those beyond longtime sitting judges, the group that Sen. Patrick Leahy (D., Vt.), the Senate Judiciary Committee chairman, has called the “judicial monastery.” Ms. Napolitano herself has been mentioned as a potential candidate, as has Sen. Amy Klobuchar (D., Minn.).

Another elected official gaining attention is California Attorney General Kamala Harris, 48, who has promoted novel crime-fighting strategies. The daughter of a Jamaican-American father and an Indian-American mother, Ms. Harris attended Hastings College of the Law in San Francisco and later was elected the city’s district attorney.

For their part, conservatives are dreading the prospect of additional appointees joining Justices Sonia Sotomayor and Elena Kagan from Mr. Obama’s first term.

On Sunday, Curt Levey, president of the Committee for Justice, a Washington, D.C., conservative legal group, emailed followers a warning headlined “Obama Court Nightmares,” illustrated with a 1957 Time magazine cover featuring Chief Justice Earl Warren. Although himself a Republican appointed by Dwight Eisenhower, Chief Justice Warren’s court handed down a raft of liberal decisions beginning with Brown v. Board of Education, which abolished school segregation. In his 2008 campaign, Mr. Obama cited Chief Justice Warren, who had been California governor and attorney general but never a judge, as exemplifying the experience he thought belonged on the Supreme Court.

Wednesday, Mr. Levey said conservatives are determined to prevent Mr. Obama from “giving us another Warren Court.”

Because Republicans lost the presidential election and a couple of Senate seats, Mr. Levey said Mr. Obama was entitled to “a lot of deference” should he wish to replace Justice Ginsburg or another liberal with a like-minded nominee.

“But if it’s replacing [Justice Antonin] Scalia or [Justice Anthony] Kennedy, then we’re really talking Armageddon”—a filibuster that could grind Washington to a halt—should the president nominate “anyone to the left of Merrick Garland,” Mr. Levey said. Judge Garland, who was considered for the earlier vacancies in Mr. Obama’s term, is a former Justice Department official who prosecuted the Unabomber, Ted Kaczynski, and Oklahoma City bomber Timothy McVeigh before President Bill Clinton appointed him to the U.S. Court of Appeals for the District of Columbia Circuit.

Mr. Obama has disappointed many liberal activists by nominating relatively few widely recognized intellectual leaders to the lower federal courts, the typical proving ground for eventual Supreme Court appointments. His effort to articulate a judicial philosophy—nominees should possess “empathy,” he asserted—was derided on the right and disclaimed even by his own first high-court nominee, Justice Sotomayor, who said at her confirmation hearing that it wasn’t a relevant factor in legal interpretation.

“I don’t think the president used much political capital on pushing for confirmation of lower court federal judges in his first term,” said Douglas Kendall, president of the liberal Constitutional Accountability Center, noting that Mr. Obama failed to get a single nominee confirmed to the D.C. appellate court, a frequent steppingstone to the Supreme Court. But “a second term is historically where legacy issues come to the fore, and there is no more important legacy than the mark left on the federal judiciary,” Mr. Kendall said.