At the center of it all is Chief Justice John Roberts, facing perhaps one of the greatest challenges of his 10-plus year tenure -- navigating a series of issues such as abortion access, health care, affirmative action and immigration with a court comprised of four liberal and four conservative justices.
Early in his tenure, Roberts said that promoting unanimity and collegiality were a priority. He's had successes in some cases and had more of a bumpy ride in others such as the 5-4 decision upholding Obamacare. How he deals with the possibility of a deadlocked court with the backdrop of a contentious election and the controversy surrounding the nomination of Scalia's replacement could say much about Roberts' leadership.
When the court is evenly divided it simply affirms the lower court opinion and sets no national precedent. It's as if the court never even heard the case.
"The chief has made clear how much he cares about preserving the court's legitimacy in these polarized times, and this term will be a real test of that vision, " said Jeffrey Rosen, president and CEO of the National Constitution Center, a non-partisan institution established by Congress.
Since Scalia's death, Roberts and his colleagues have worked to find common ground or move quickly where possible. The court has already announced that it was deadlocked in an important case concerning public sector unions as well as two others.
It managed a unanimous result in a voting rights case, brought by conservative activists. It issued an order in a voter ID case that reflected a goal for consensus on an issue that might come back as the election heats up. And justices sent a clear signal that they are working overtime trying to find a way forward in a contraceptive mandate case.
Justice Elena Kagan, a liberal, gave Roberts early praise for how he's handled the court and worked to build consensus since Scalia's death in February.
"I think he's conveyed that both in his words and in his deeds to all of us and I give him enormous credit for what he's doing," she said at NYU Law School last month.
Roberts has steered clear of discussing controversial topics in public. Last week, at a judicial conference in Arkansas, he was asked whether he'd like to expand upon comments he made before the death of Scalia concerning the politicization of the confirmation process.
According to the Washington Post, Roberts had a simple answer: No.
Although he's the chief of the court that bears his name, he only has one vote. But he serves as a traffic cop on an increasingly hot bench, and he runs the closed-door conference where decisions are made.
As chief, he has the power to assign opinions if he is in the majority. "It's not my greatest power; it's my only power," Roberts told Rosen for an article he wrote for The Atlantic in 2007.
"The chief's ability to frame the debate behind closed doors by speaking at conference can make a huge difference," Rosen said.
Impact of a 4-4 court
Kagan repeated the refrain that while the court is often unanimous, the media and the public often focus solely on the handful of 5-4 decisions that occur each term.
What makes this term different, however, is that with Scalia's absence in some of those 5-4 decisions could become 4-4.
"Although sharply divided decisions in prior terms (i.e., 5-4) might have perpetuated the perception of an ideologically divided court, sharply divided decisions this term (i.e., 4-4) come with an added twist: no decision of the court at all," said Pratik A. Shah, a lawyer at Akin Gump who frequently argues before the court.
As the stalemate continues in Washington over whether the Republicans will hold confirmation hearings for Judge Merrick Garland, it's unclear when the court will return to full strength.
Democrats have used the prospect of more 4-4 rulings as an argument Garland should be confirmed. The inability to set national precedents deprives people in parts of the country the full protections of the law, they argue. Republicans have downplayed the impacts of those rulings, and stressed a belief that there should be no hearings so close to an elections.
The court has already accepted fewer cases for next term, perhaps because justices are unclear of how long they will remain without a replacement for Scalia.
Working to find consensus
Justices have worked to find consensus whenever possible.
For instance, after oral arguments in a challenge to the Affordable Care Act's contraceptive mandate it seemed the justices might be headed for an even split. But a few days later the court issued an unusual order suggesting it was seeking compromise in the case.
The justices took a narrow route that managed to win the support of the full court, when they ruled in a case concerning the drawing of state legislative lines in Texas.
And a recent order reflected sensitivity to a challenge that divided the justices two years ago.
At issue was an emergency motion brought by civil rights groups to block Texas' controversial voter ID law even before the challenge could be heard by a federal appeals court. The first time the law came before the court in 2014, the justices allowed it to remain in effect over a harsh dissent penned by Justice Ruth Bader Ginsburg and joined by Justice Sonia Sotomayor and Kagan. This time around, the justices once again allowed the law to remain in effect, but the court's order made clear that if the appeals court didn't act in a timely matter, the plaintiffs could return to the high court for relief.
There are only a few tea leaves on how they might rule in some of the other cases.
The affirmative action case, for example, will be decided by seven justices because of Scalia's death and the fact that Justice Kagan had to recuse herself from hearing the challenge because she dealt with it in her previous job. Behind closed doors, the chief might question whether the case would be a good vehicle for a broad 4-3 ruling.
"I would be kind of surprised almost if this winds up being that consequential a case because I think the chief justice might feel a little bit chary about having much decided by a seven-member divided court by a single vote," lawyer John Elwood said at an event sponsored by the Constitutional Accountability Center.