Now that a federal appellate court in San Francisco has upheld an order temporarily halting President Donald Trump's travel ban, experts say it's all but certain the president will appeal the decision to the United States Supreme Court.

Less certain is whether the justices are willing to hearing more arguments on whether the temporary restraining order should be lifted -- or how the short-handed court would rule if it did.

That's because the restraining order halting Trump's ban of immigrants from seven Muslim-majority countries revolves around thorny, as-yet-unsettled questions relating to national security, religious discrimination and constitutional law, set against a background of hardball politics and nationwide dissent.

Although the Justice Department said it's reviewing its options, "I'd be surprised if the administration doesn't appeal to the Supreme Court," says Adam Winkler, a constitutional law professor at the University of California-Los Angeles.

But "I wouldn't predict it would be a 4-4 split necessarily," Winkler says. "It's hard to know exactly what they will do. There are a lot of options for the Supreme Court."

In a spate of lawsuits around the country, judges on both the left and right side of the political spectrum "have ruled against various parts of the travel ban," says Winkler. "While this is a partisan issue, I don't think the partisan line is likely to divide judges as much."

But Melissa Hart, a law professor at the University of Colorado, says it's not a lock that the high court would accept a case whose merits haven't been argued yet.

"These things are never totally easy to predict. It's extremely unusual for a case to go to the Supreme Court at this early stage," says Hart, director of the Byron R. White Center for the Study of Constitutional Law.

"Some more airing of the merits in the lower courts is probably appropriate" before the high court hears arguments on the 9th Circuit's ruling upholding the temporary restraining order, Hart says. "There may be some reluctance on the court to take this up when there are only eight justices" and the possibility the court would deadlock on a case that has global ramifications.

"It's obviously an issue of national importance," says Hart. "Is it an issue of such importance that the Supreme Court has to step in right now? That's the question."

If the Supreme Court refuses to hear the case, then the federal appellate court decision stands.

Thousands Protest Immigration Ban View All 25 Images

On Thursday, a three-judge panel of the federal 9th Circuit Court of Appeals unanimously rejected the Trump administration's argument that a lawsuit blocking the president's executive order banning immigrants from seven Muslim-majority countries was a threat to national security.

The order -- a high-stakes collision of presidential authority, national security and foreign policy -- sowed chaos around the country when Trump implemented it just days after his inauguration. As protests against the ban erupted in airport terminals, immigration lawyers around the country sued to stop the sweeping order.

Federal judges around the country blocked some parts of the president's executive order, but the states of Washington and Minnesota sued the government. On Feb. 3, Judge James Robart in Seattle agreed to temporarily suspend the order until the merits of the case are sorted out in a lower court and the 9th Circuit upheld that decision.

Though the Justice Department, under new Attorney General Jeff Sessions, has taken a cautious approach so far, Trump was characteristically defiant. When the 9th Circuit ruling was announced, he tweeted, "SEE YOU IN COURT, THE SECURITY OF OUR NATION IS AT STAKE!" Friday morning, he tweeted that the ruling was "a disgraceful decision."

SEE YOU IN COURT, THE SECURITY OF OUR NATION IS AT STAKE! — Donald J. Trump (@realDonaldTrump) February 9, 2017

LAWFARE: "Remarkably, in the entire opinion, the panel did not bother even to cite this (the) statute." A disgraceful decision! — Donald J. Trump (@realDonaldTrump) February 10, 2017

But several experts say the political dynamics surrounding the case -- including Republicans' own decision to block President Barack Obama from replacing the late Justice Antonin Scalia, who died suddenly on a luxury hunting trip a year ago -- make it a tough strategic read for the government's lawyers, and an uphill climb if the high court agrees to hear the case.

"We're talking in a sense here about two cases," says Russell Wheeler, a senior fellow at the Brookings Institute and a law professor at American University. At this stage of the proceedings, he says, "it's not so much about the legality of [Trump's executive order], but whether or not to keep in place the stay."

Wheeler notes that in 2014, Obama's immigration order allowing millions of immigrants without documentation to stay in the U.S. reached the court not long after it was implemented. But the court, absent Scalia, deadlocked in a 4-4 decision, and they're not likely to want to repeat the experience on such an important issue, Wheeler said.

If the Supreme Court takes a pass, "The decision of the lower court stands uninterrupted," Wheeler says. But the administration has another option: Request an en banc rehearing in the 9th Circuit before a full, 11-judge panel.

"If you lose in the [3-judge] panel, you ask the full [appellate] court to look at it again," Wheeler says.

For the government to win the appeal at that stage, it would have to prove that "pausing and evaluating the legality of the order is hurting the government," says the University of Colorado's Hart. "That's a tough argument for the government to make."

By contrast, "people who have gone through the elaborate process" of being screened before entering the U.S. are "irreparably harmed [by the ban] by being forced to go back to countries that they are fleeing from," says Hart.

During the arguments before the three-judge panel, "it seems like the government's lawyer did have a very challenging time," UCLA's Winkler says. "He was even saying at one point, 'My argument does not appear to be convincing the justices.'"

In its unsigned opinion, the three-judge panel strongly suggested that hitting the pause button on Trump's executive order is not a threat to national security, declaring the government in its arguments had presented "no evidence" that anyone from the seven nations had committed terrorism in the United States.

That declaration could make it tough to persuade the Supreme Court to lift the stay on Trump's executive order, experts say: The stay is temporary, and the substantive challenges to the executive order -- including allegations that, by targeting Muslim nations, Trump has created a religious test for immigrants in violation of the Constitution -- are still undecided.

At this stage, "the courts are not going to decide the underlying merit" of the travel ban itself, Winkler says.

Nevertheless, it's highly possible that an eight-member court could rule decisively on the issue -- perhaps to send a message about the Constitutional separation of powers to a new president, Winkler says.

Given Trump's ongoing criticism of the federal judiciary in the case, "it's more likely that conservative judges will rule against him," Winkler says. "Judges take the power of the judiciary very seriously. And neither conservative judges nor liberal judges really enjoy the executive branch undermining power of the courts."

Ultimately, if the government's appeal of the temporary restraining order falls short, "I think it's for sure that the underlying case [challenging Trump's order] will get to the Supreme Court," says the Brookings Institute's Wheeler.