All eyes are on Justice Neil Gorsuch as a major constitutional challenge to one of President Trump's most controversial initiatives -- the so-called travel ban -- comes before the Supreme Court.

Trump's own nominee to the court could prove key with oral arguments scheduled for Wednesday.

At issue, in part, is whether the third and latest version of Trump's travel ban, affecting visitors from six majority Muslim nations, discriminates on the basis of nationality and religion. Given the high public interest, the court is modifying its usual policy and will release audio of the session soon after its conclusion.

The controversy pits an administration that considers the restrictions necessary for Americans' security against challengers who claim it is illegally aimed at Muslims -- and stems from Trump's campaign call for a "total and complete shutdown of Muslims" entering the U.S.

The case will be the first significant legal test so far of the president's administration and could lead to a precedent-setting ruling on the limits of executive power, especially within the immigration context.

"This is a very difficult issue for the Supreme Court," said Thomas Dupree, a former top Bush Justice Department official. "In many ways, it's a political judgment -- who is allowed into this country -- and historically the court has been very reluctant to tread into areas where it could be viewed as making a political judgment that is properly confined to the executive."

The Gorsuch factor

Attention on Gorsuch is heightened after a surprise ruling last week. Trump's appointee to the high court has been a reliable conservative in his first year on the bench but last week ruled against the administration in a separate immigration case involving government efforts to deport foreigners convicted of serious crimes in the U.S.

Gorsuch in that dispute sided with the court's four more liberal members, the first time that has happened in his tenure on the job. He has given no indication how he would vote in the travel ban issue.

In this case, the justices have allowed the current restrictions -- known as travel ban 3.0 -- to be enforced at the Justice Department's request, at least until the case is fully litigated.

Federal appeals courts in Virginia and California in recent months had ruled against the administration. The San Francisco-based 9th Circuit court last December concluded Trump's proclamation, like the two previous executive orders, overstepped his powers to regulate the entry of aliens.

It "fails to provide a rationale explaining why permitting entry of nationals from the six designated countries under current protocols would be detrimental to the interests of the United States," wrote the appeals judges.

The White House, on the other hand, has framed the issue as a temporary move involving national security. A coalition of groups in opposition call the order blatant religious discrimination, since the six countries involved have mostly Muslim populations: Iran, Libya, Somalia, Sudan, Syria and Yemen.

How much power does the president have?

A major sticking point for the justices will be navigating how much discretion the president really has over immigration. Courts have historically been deferential in this area, and recent presidents from Jimmy Carter to Ronald Reagan to Barack Obama have used it to deny entry to certain refugees and diplomats, including nations such as Iran, Cuba and North Korea.

A 1952 federal law -- the Immigration and Nationality Act, passed in the midst of a Cold War fear over Communist influence -- historically gives the chief executive broad authority.

It reads in part: "Whenever the president finds that the entry of any aliens or of any class of aliens into the United States would be detrimental to the interests of the United States, he may, may by proclamation, and for such period as he shall deem necessary, suspend the entry of all aliens or any class of aliens as immigrants or nonimmigrants, or impose on the entry of aliens any restrictions he may deem to be appropriate."

The administration strongly denies this is a "Muslim ban," but federal judges across the country cited statements by then-presidential candidate Trump and his advisers, including a December 2015 campaign press release calling for such restrictions, citing "hatred" by "large segments of the Muslim population."

In its legal brief to the high court, the Justice Department downplayed the impact of remarks made by a candidate for high office.

"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," wrote the department's Solicitor General Noel Francisco.

Sixteen state leaders led by Texas are among a number of coalitions backing the Trump administration.

But Hawaii officials, who filed the appeal contesting all of the president's orders, say the president's policies continue to violate the Constitution's guarantee of religious freedom:

"Any reasonable observer who heard the President's campaign promises, read his thinly justified orders banning overwhelmingly Muslim populations, and observed his Administration's persistent statements linking the two, would view the order and each of its precursors as the fulfillment of the President's promise to prohibit Muslim immigration to the United States."

A number of civil rights, immigrant and Muslim advocates filed separate briefs opposing the government's policies. These challengers to the 3.0 order argue Trump has taken his enumerated powers to extremes by banning entire populations from multiple countries, an estimated 150 million people.

Legal experts say the high court will be juggling multiple issues.

"This ban does not make us safer," said Elizabeth Wydra, president of the progressive Constitutional Accountability Center. "In fact, it actually goes against our national security because it undermines key elements of our Constitution: the idea we don't discriminate on the basis of religion. There cannot be a religious test at the border. That's un-American, unconstitutional and unlawful."

But conservatives say the justices should have a limited role here.

"If you don't like the policy prescriptions of a president, you vote him out of office. It is not the judiciary's role to look behind the executive order," said Gayle Trotter, a Washington attorney and columnist. "He has the authority, particularly in this area where his powers are at the height under the Constitution."

Trump's first executive order was issued just a week after he took office, and was aimed at seven countries. It triggered chaos and protests across the U.S., as some travelers were stopped from boarding international flights and others detained at airports for hours. Trump modified the order after a federal appeals court refused to allow the ban to be enforced.

"This is not about religion-- this is about terror and keeping our country safe," said the president on Jan. 29, 2017.

The next version, unveiled weeks later, dropped Iraq from the list of covered countries and made it clear the 90-day ban covering Iran, Libya, Somalia, Sudan, Syria and Yemen didn't apply to those travelers who already had valid visas. It also got rid of language that would give priority to religious minorities. Critics said the changes did not erase the legal problems with the ban.

When that second temporary travel ban expired in Sept. 24, it was replaced with Proclamation 9645 -- what the administration said was a country-by-country assessment of security and cooperation with the U.S.

The current case is Trump v. Hawaii (17-965). A ruling is expected by the end of June.