By Ariane de Vogue, CNN Supreme Court Reporter

(CNN) -- More than a year after President Donald Trump caused chaos in the airports by following through on a campaign promise and restricting travel from several Muslim-majority countries, the Supreme Court is poised to hear arguments on the legality of a third version of the original travel ban and decide whether the President ultimately exceeded his authority.

After various iterations of the ban ricocheted through the courts, the Supreme Court agreed last December to allow travel ban 3.0 to go entirely into effect pending appeal.

Now, the nine justices -- five appointed by Republican presidents and four appointed by Democrats -- will finally get their chance to weigh in on a centerpiece of Trump immigration policy.

Supporters of the President say he acted to protect the country's national security. But critics say the travel ban represents executive overreach, lacks justification and amounts to an illegal ban on Muslims.

The version of the ban before the court, signed in September, came after the administration completed a worldwide review as to the vetting procedures of several countries. The ban restricts the entry of noncitizens from seven countries to varying degrees: Iran, North Korea, Syria, Libya, Yemen, Somalia and Venezuela. (Chad has been removed from the list.)

Challengers of the ban argue that it is "an order without parallel in our nation's history" and that it amounts to a "sweeping and unilateral order that purports to ban over 150 million aliens -- the vast majority of them Muslim -- from entering the United States."

The challengers are represented by former Acting Solicitor General Neal Katyal and include the state of Hawaii, and individuals currently living in the United States. In court briefs, Katyal argues that the proclamation exceeds the President's authority under immigration law as well as the Establishment Clause of the Constitution.

"If the President possessed the power he claims, he could eradicate Congress's immigration laws with the stroke of a pen, and usurp virtually the whole of the immigration power that the Founders vested in Congress to secure liberty," Katyal argued.

Katyal relies on a "litany" of statements that Trump made during the campaign and afterward concerning a restriction of Muslims entering the United States and notes that even though the current proclamation was crafted after a review of the entry policies of other governments, it is a "direct descendant of previous bans" covering many of the same countries.

His brief includes some of the President's statements on the campaign trail calling for a "Muslim ban" as well as a retweet of three anti-Muslim propaganda videos he sent on November 29, 2017.

The administration rejects any claim, despite the fact that the majority of countries affected are Muslim majority, that religion is in play and argues that several lower courts that pointed to the President's campaign statement regarding a so called "Muslim ban" were wrong to do so.

"Impugning the official objective of a formal national-security and foreign policy judgment of the President based on campaign-trail statements is inappropriate and fraught with intractable difficulties," Solicitor General Noel Francisco wrote in court papers.

He even nodded to the President's tweets and said "the President's retweets do not address the meaning of the Proclamation at all."

Francisco acknowledges that many of the countries at issue in travel ban 3.0 were also part of earlier travel ban iterations but says that unlike those versions, the current ban benefits from a lengthy review, it targets both Muslim majority and non-Muslim-majority countries, and its restrictions are tailored to each country.

Justices to watch

Court watchers will train their attention on Justice Anthony Kennedy, who could play a critical role, especially as the justices decide whether they should consider alleged animus on the part of the President. In 2015, Kennedy wrote a concurring opinion in a case concerning a US citizen's claim that she deserved more information for a consular officer's denial of a visa for her husband. Kennedy suggested that sometimes -- if there is bad faith -- the government's motives can be subject to legal review.

Others note that while Justices Ruth Bader Ginsburg and Sonia Sotomayor publicly dissented from the order allowing the ban to go fully into effect, liberal Justices Elena Kagan and Stephen Breyer chose not to.

While that may reflect the fact that they think the ban passes muster, it could also mean they didn't think irreparable harm would be caused if they allowed the ban to go into effect while the case was under consideration.

Justice Neil Gorsuch will be in the spotlight too, as he reviews a central policy of the man who nominated him to the bench.

Both sides say that if the court greenlights the ban it will send a strong message for other presidents and could shed light on how courts should consider statements a president makes during a campaign or on his Twitter feed.

"Nobody denies that the president wields extraordinary power over immigration and national security," said Joshua Matz, who sided with the challengers in a brief filed on behalf of constitutional scholars. "What's at stake here is the president's ability to evade any legal consequence for his own public statements, including those broadcast on a global stage."

Joshua A. Geltzer of Georgetown Law, who also opposes the ban, says the case is about the office of the president, not any one president. "It's about whether our federal courts have a meaningful role to play in enforcing the limits of those authorities, or whether -- as the government argues here -- the courts simply shouldn't be looking at this at all," he said.

Josh Blackman, a law professor at the South Texas College of Law in Houston, believes the justices will find that the travel ban passes legal muster.

"If the court upholds the travel ban on statutory grounds, it will signal that Congress has for decades vested the president with the flexibility to respond to an unforeseeable national security dynamic," he said.

Blackman thinks the court will find that the President has his own inherent constitutional authority to exclude noncitizens and the justices won't hold campaign statements against the President.

"If the Supreme Court rules that the President's actions can be halted based on his campaign statements, courts will be drawn into the unenviable position of serving as fact-checkers for the executive branch," he said.

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