WASHINGTON – The late Chief Justice William Rehnquist was a busy man on Jan. 20, 1999. The impeachment trial of President Bill Clinton was in its second week, and Rehnquist had to stop presiding over an oral argument at the Supreme Court, cross the street, and preside over the Senate.

One of the lawyers arguing before the high court that day was John Roberts. Once one of Rehnquist's law clerks at the high court, Roberts could be juggling the same two jobs as his former boss soon.

President Donald Trump was impeachedby the House of Representatives on Wednesday and will be tried by the Senate. That means it will be Roberts, nominated by President George W. Bush to succeed Rehnquist as chief justice in 2005, presiding, as called for by the Constitution.

Those who know the chief justice best say he's a perfect fit for the job.

"I've argued in front of him 39 times, and I think what comes across is that he cares deeply about institutions," says Neal Katyal, a former acting U.S. solicitor general who, like Roberts before him, heads appellate litigation at Hogan Lovells.

Like Rehnquist – who once quipped that as the Clinton impeachment trial's presiding officer he "did nothing in particular and did it very well" – Katyal says Roberts would "work hard to be scrupulously fair in carrying out a unique constitutional function."

New term:Supreme Court, trying to remain above the partisan fray, opens 2019 term with a debate about insanity

Last term:Supreme Court in transition: Conservatives ascendant but Roberts, Gorsuch, Kavanaugh prove unpredictable

Roberts, 64 and in his 15th term as chief justice, now sits in the middleof the Supreme Court figuratively as well as literally. With the retirement of Associate Justice Anthony Kennedy last year, he has become the closest thing to a swing vote between four conservative and four liberal justices.

Balls and strikes

Roberts' last tango with the Senate came in 2005, when he defined the chief justice's role as that of an umpire calling balls and strikes en route to his 78-22 confirmation. Since then, he has tried to keep the Supreme Court out of politics – not always with success.

When Trump criticized an "Obama judge" last year over an immigration ruling, Roberts issued a rare rebuke. "We do not have Obama judges or Trump judges, Bush judges or Clinton judges," he said. "What we have is an extraordinary group of dedicated judges doing their level best to do equal right to those appearing before them."

During an appearance in New York City in September, Roberts said that appraisal applies to the justices as well.

“When you live in a politically polarized environment, people tend to see everything in those terms," he told about 2,000 people at Temple Emanu-el in Manhattan. "That’s not how we at the court function.”

In absentia, it would be Trump appearing before Roberts in a Senate impeachment trial, but the chief justice's role is more umpire than judge or jury. The Senate would acquit or convict the president; Roberts would rule on procedural matters and might break tie votes, but not on conviction, which requires a two-thirds majority of the 100-member Senate.

“I believe his presence would have a positive influence on the tenor of any debate,” says Walter Dellinger, a former acting U.S. solicitor general during the Clinton administration who argued the other case before the Supreme Court on Jan. 20, 1999. He recalls the marshal advising the advocates that Rehnquist would be leaving promptly at 11:50 a.m., and "not to take it personally."

"It would be fortunate to have Chief Justice Roberts preside over an impeachment trial, because I think he’ll be perceived to be fair and restrained," Dellinger says.

Live television

Restraint might be difficult in the current political environment, however. Richard Lazarus, a Harvard Law School professor and Roberts' roommate when both were students there in the 1970s, says Senate Democrats and Republicans worked together to set rules for the Clinton trial. That may be harder this time around.

“He knows that when he crosses First Street, he's going to be putting himself right in the middle of the workings of the political branch," Lazarus says. "He’s going to work hard to keep above the fray.”

In addition to partisan rancor, Roberts also would have to get used to being on live television – "the very thing that all the justices, certainly the chief, have not wanted to happen in the Supreme Court," Lazarus says.

There was no live TV in 1868, when Chief Justice Salmon Chase presided over the Senate's first impeachment trial of President Andrew Johnson. That was a good thing for Chase, who had two of his procedural rulings overruled.

Rehnquist did not meet that fate in the Senate's second impeachment trial, but his most significant ruling was to stop House members serving as managers, or prosecutors, from calling senators "jurors."

In a third Senate presidential impeachment trial, Roberts similarly would hope to avoid substantive rulings, Dellinger says. But he could be drawn into disputes over the admission of evidence or other matters.

"While they may be overturned by the vote of the Senate," Dellinger says, the chief justice's rulings "nonetheless would come with some moral force.”