WASINGTON —  Chief Justice John G. Roberts Jr. will almost certainly try to keep a low profile in the upcoming impeachment trial of President Trump.

But given the lack of a bipartisan agreement in the Senate, Roberts may find himself nevertheless called upon to weigh in on the most difficult questions, including whether witnesses will testify.

For only the third time in American history, the chief justice will carry out one of the special duties assigned to him by the Constitution. The framers of 1787 foresaw that the vice president, who usually presides over the Senate, would have a clear conflict of interest, since he would assume the highest office if the president were convicted by two-thirds of the senators.

Most legal experts expect Roberts will have a largely ceremonial role rather than a pivotal one in shaping the trial. Neither the Constitution nor historic precedents make clear how the “presiding officer” should conduct an impeachment trial.

On the one hand, the Senate “shall have the sole power to try all impeachments,” according to the Constitution, and this includes setting rules for the trial as well as making the ultimate decision on the president’s guilt.

At the same time, the Senate’s long-standing rules say “the presiding officer shall have the power to make and issue” orders for conducting the trial, and he “may rule on all questions of evidence, including but not limited to questions of relevance [and] materiality.”

The senators, by majority vote, can settle many procedural questions in advance by passing a rules package that spells out when a trial begins, how long it will last, how much time each side has and what evidence can be offered, including witnesses. During the Clinton impeachment, both sides agreed on such a pretrial rules package, which among other things determined that the question of witnesses would be postponed until after the trial was underway.

But Senate Majority Leader Mitch McConnell (R-Ky.) said this week that he is prepared to begin Senate proceedings without an agreement with Democrats on key issues, such as witnesses. He said he has enough GOP votes to approve rules that would put off any decision about witnesses until after the trial is underway, something Democrats oppose.

If that happens, expect Democrats to turn to long-standing Senate impeachment rules that give the chief justice authority to decide, at least in the first instance, questions “with respect to the admission of evidence.” Among other things, House managers are likely to ask Roberts to require testimony from former national security advisor John Bolton.

But there’s an important caveat. The chief justice’s “ruling shall stand as the judgment of the Senate,” the rules say, unless a senator asks for a vote to overturn his decision. In other words, any senator can demand that any of the chief justice’s rulings be put to a floor vote, and a simple majority can overrule that decision. For that reason, the chief justice lacks the most basic power of other judges, since his rulings effectively can be overturned by the jury.

The rules give the chief justice a way to avoid such an embarrassing rebuff. Rather than decide a contentious matter when asked, the presiding officer can essentially punt. The same rule goes on to say the presiding officer “may at his option, in the first instance, submit any such question to a vote” of the Senate.

For guidance on his role, Roberts has only two precedents to study: the 1868 trial of Andrew Johnson when Chief Justice Salmon Chase was in the chair, and the 1999 trial of President Clinton when Chief Justice William H. Rehnquist presided.

Chase was a former senator, governor and past presidential contender, and he had his eye on the presidency again in 1868. He was criticized then and by historians since for seeking to dominate the Senate trial, even breaking a tie vote when senators were split on an issue.

Rehnquist, if anything, erred in the other direction. In 1992, he had written a history of the failed impeachments of early Supreme Court Justice Samuel Chase and Andrew Johnson, and he concluded both would have damaged the independence of the high court and the presidency had they succeeded. He took a minimal role in the Clinton trial and left it to the senators to shape the trial.

“I did nothing in particular, and I did it well,” Rehnquist said afterward, quoting a Gilbert and Sullivan character.

At first glance, it would appear that Rehnquist would serve as the model for a chief justice who wants to avoid partisan conflict.

Roberts, who will turn 65 later this month, first arrived in Washington 40 years ago to work as a law clerk for then-Associate Justice Rehnquist. He had grown up in Indiana, excelled in college and law school at Harvard and spent a year as a law clerk for a prominent appeals court judge in New York.

He developed a deep admiration for Rehnquist, who helped launch his career as a lawyer in the incoming Reagan administration and later as a leading advocate in the Supreme Court. When Rehnquist died in 2005, Roberts succeeded him as chief justice.

Yale law professor Akhil Amar said Roberts will almost surely be guided by Rehnquist’s hands-off approach.

“He will have studied the Rehnquist precedent, and he doesn’t want this to be about him,” Amar said. “He’s a Republican’s Republican, but he doesn’t see himself as a hyper-partisan. He’s perceived as neutral. If the Senate is equally divided, he has some running room, but I would be very surprised if the chief justice tries to take over the show. If it turns into a partisan fight where everyone is throwing mud, he will do the smart thing, which is to duck.”

Elizabeth Wydra, president of the Constitutional Accountability Center, said Roberts could be “put in a terrible position.” As a chief justice, he has tried to keep the Supreme Court separate from politics and the partisan battles of Washington, but he could be easily drawn into a partisan fight.

Nonetheless, she said, “he has a vested interest in presiding over a fair trial because he realizes how this could influence how the public perceives the high court.”

Sarah A. Binder, a Brookings Institution expert on Congress, said the rules for an impeachment trial put power in the hands of the senators, not the presiding officer. “I don’t get the sense that Roberts wants to be making pivotal decisions,” she said. “And any senator can challenge and immediately secure a vote to challenge one of his rulings.”

It is not clear, however, whether McConnell can count on all of the Senate’s 53 Republicans to vote together, particularly on such things as whether to have testimony from witnesses. “Ultimately, the powerful player here is whoever makes that 51st vote to uphold or overturn a Roberts decision,” she said.

Others say Roberts may play a pivotal rule because the Senate is so closely split.

“He would probably like to play the Rehnquist role, but then there was an agreement in advance” by the Republican and Democratic leaders of the Senate, said former White House counsel Neil Eggleston, who worked on Clinton’s defense in the 1999 trial. Those bipartisan agreements settled most of the key questions in the trial, avoiding the need for Rehnquist to get involved.

“This time it will not be resolved in advance. And the rules give the chief justice a lot of power to rule on evidence, which includes calling witnesses,” he said.

Senators, he said, may be reluctant to use their power to challenge his decisions. “They could overrule the chief justice, but that would not look good,” Eggleston added.

Georgetown law professor David A. Super agreed Roberts might find himself in a tough spot, trying to balance his responsibilities as a judge with his desire to stay out of controversy.

“If the House managers ask for subpoenas, that is a routine decision for a trial judge,” Super said. “I think he would not want to be perceived as undermining the trial by avoiding a decision. If he ducked a decision, it could look like he was part of McConnell’s effort to coordinate with the White House.”

“I also think he takes very seriously the Constitution’s allocations of power,” he said, “and the framers made him the presiding officer in an impeachment trial.”

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