But, similar to a debate that has consumed Washington, D.C., for the past 15 months, a major issue for the court is separating "the president" from "this president."
The justices on Wednesday will consider President Donald Trump's third iteration of a travel ban that bars most nationals from a small group of mostly Muslim nations. It is the first time the court has considered the merits of a policy that has consumed the administration since its start, and raises deep questions about the judiciary's role in national security issues usually left to the political branches.
The first version of the ban was issued just a week after Trump took office, and lower courts have found that it and each reformulated version since has exceeded the authority granted by Congress and was motivated by Trump's prejudice - animus, as courts like to say - toward Muslims.
The state of Hawaii, which is leading the challenge of the ban, told the Supreme Court:
"For over a year, the president campaigned on the pledge, never retracted, that he would ban Muslims from entering the United States.
"And upon taking office, the president issued and reissued, and reissued again, a sweeping and unilateral order that purports to bar over 150 million aliens - the vast majority of them Muslim - from entering the United States."
Hawaii's brief, by Washington lawyer Neal Katyal, cites not only Trump's campaign comments but also his actions as president, including the time he retweeted "three anti-Muslim propaganda videos" from a widely condemned far-right British organization.
This led to a response by the solicitor general of the United States to the justices of the Supreme Court that could only have been written in this era, about this chief executive:
"The president's retweets do not address the meaning of the proclamation at all."
Solicitor General Noel Francisco urged the court not to get distracted by the president's bluster - he's said nice things about Muslims, too, the brief states - and to keep its examination on the law.
"The Constitution and acts of Congress . . . both confer on the President broad authority to suspend or restrict the entry of aliens outside the United States when he deems it in the nation's interest," Francisco wrote.
If the president's comments and tweets were not a factor, many legal experts said the court would likely extend the deference to the political branches it has shown in the past when considering issues of immigration and national security.
Washington lawyer Gregory Garre, who defended executive authority as President George W. Bush's solicitor general, said the law makes such respect clear.
"No matter where the court ends up, the president starts with two significant pluses - the executive's inherent constitutional authority over foreign affairs and a textually broad grant of authority by Congress to regulate the entry of aliens determined to be detrimental to the interests of the United States," Garre said.
Los Angeles lawyer Theodore Boutrous agrees, with a caveat: But Trump.
"This case comes to the court with this backdrop of a president who has been shattering norms, even brazenly saying they don't matter," said Boutrous, who filed a brief on behalf of the U.S. Conference of Catholic Bishops urging the court to strike down the ban.
His brief on behalf of the bishops said that the travel ban is a result of "blatant religious discrimination" and that it "poses a substantial threat to religious liberty that this court has never tolerated before and should not tolerate now."
Trump's efforts to ban certain travelers has a complicated backstory. He first issued a proclamation banning travel from certain countries a week after taking office. It went into effect immediately, causing chaos and protests at airports around the world.
The U.S. Court of Appeals for the 9th Circuit issued an injunction. Instead of appealing to the Supreme Court, the administration enacted a second version of the plan. That was stopped by two regional courts of appeals.
Before the Supreme Court could consider the merits of the second plan, the administration in September announced a new one.
It blocked entry into the United States of most people from Chad, Iran, Libya, Somalia, Syria and Yemen, and certain visitors from North Korea and Venezuela. The latter two countries are not part of the challenge before the Supreme Court, and the administration on April 10 removed Chad from the list.
Francisco told the court that the third edition of the ban responds to the criticisms by lower courts of the first two, and was the result of a "worldwide review of the processes for vetting aliens seeking entry from abroad."
The resulting ban was no different from what past presidents have occasionally imposed, he said. Congress specifically has granted authority that the president "may by proclamation, and for such period as he shall deem necessary, suspend the entry of all aliens or any class of aliens" after a finding that the entry "would be detrimental to the interests of the United States," Francisco wrote.
But challengers to the ban point to another section of the law, which says a person may not be denied an immigration visa "because of the person's race, sex, nationality, place of birth, or place of residence."
Allowing the president to ban citizens of a nation, the challengers said, amounts to giving the president a "line-item veto over the entire immigration code."
Besides examining the immigration statute, the court has said it will review the decision of the U.S. Court of Appeals for the 4th Circuit that the ban violates the First Amendment's guarantee against religious discrimination.
And the court will also consider whether the judiciary even has authority to "look behind" the face of an immigration proclamation to examine whether it was drawn with improper motives.
Again, the court was urged to look beyond Trump.
"The scope of this court's decision here will have an impact on this (and future) president's ability to protect our national security interests as he (and Congress) sees fit," said a brief filed by national security experts supporting Trump. "At the end of the day, it is not the role of the judiciary to intercede in such matters, and this court should clearly say so."
The challengers are backed by a large number of organizations that contend otherwise. Religious groups say it is the job of the court to guard constitutional protections against religious discrimination. Universities say the ban harms them in recruiting students and scholars. A different set of national security experts say the ban will harm U.S. interests in the long run.
The libertarian Cato Institute says its research leads to the conclusion that the ban is based more on discrimination than protection.
"Not a single person from these countries has killed anyone in a terrorist attack in the United States in over four decades," the brief stated. "Nationals of the designated countries have also been much less likely to commit other serious crimes than U.S.-born persons or other foreign nationals."
The justices may have already signaled that they are inclined to rule for the administration. In December, the court issued a stay of a lower court's injunction and allowed the ban to take effect, with only Justices Ruth Bader Ginsburg and Sonia Sotomayor noting their objections.
Josh Blackman, a professor at the South Texas College of Law in Houston, said only once in the more-than-a-decade Roberts court have the justices granted a stay without later reversing the opinion of the lower court.
In a conference call with reporters sponsored by the Federalist Society, Blackman predicted the same would happen in this case. But he, too, addressed the question of how the court would view Trump, and made his case for reversing the lower courts in a way it is unlikely the Trump administration itself would endorse.
"If the court rules here for President Trump, I don't see that many lingering problems; I don't know that we'll ever have a president again like Trump, who says such awful, awful things on a daily basis," Blackman said.
"I worry much more if they rule against President Trump, and they give courts green light to parse campaign statements and the like, this could potentially hamstring not just this president but also future presidents."
The case is Trump v. Hawaii.