ABC News took a look at three possible outcomes of the case:
What Happens if Appeals Court Declines to Lift the TRO?
Robart has set an expedited schedule on the state's request for a preliminary injunction, which, if granted, will result in a longer-lasting hold on the executive order and could remain in place until the case is resolved. He ordered the two states to submit arguments for the preliminary injunction by the end of day Thursday, and all legal briefs from the parties are due to be submitted by the end of next week. The anticipated pace of those proceedings may be a factor in the appellate panel's decision — particularly if they are inclined not to disturb the lower court ruling, says ABC News' legal analyst, Dan Abrams.
"The faster the lower court seems ready to resolve this, the more likely that the appellate court will say, 'It is just a TRO. Let's just play it out,' Abrams said before the hearing. "I would think that if the court says, 'Too early or not enough here to overrule it,' that they are absolutely going to be inviting a return at a date not that far into the future."
During oral arguments on Tuesday afternoon, Circuit Judge Michelle Friedland, an Obama appointee, pointedly questioned the federal government's decision to appeal the TRO at such an early stage of the lower court case.
"You're saying that the proceedings are moving fast, but you appealed to us before you continued in the district court to develop the record," said Friedland, "so why should we be hearing this now if it sounds like you're trying to say you're going to present other evidence later?"
"The reason we sought immediate relief and a stay is because ... the district court's decision overrides the president's national security judgment about the level of risk," Flentje said. "It should be acknowledged that ... the president is the official that is charged with making those judgments."
What Happens if the Appeals Court Lifts the TRO?
If the appellate court sides with the Trump administration and orders the district court to lift the TRO, then the executive order could go back into effect, at least for the time being.
Washington state’s Solicitor General Noah Purcell argued that lifting the restraining order could once again result in widespread uncertainty about the application and enforcement of the executive order.
"At this point it's really the federal government that's asking the court to upset the status quo," Purcell said. The government is asking "to reinstate the executive order without full judicial review and throw this country back into chaos. The court should decline that invitation," he argued.
Even if the appellate court decides to lift the restraining order, the district court still take up the request from the plaintiff states for a preliminary injunction.
But could Robart block the ban again?
"That's entirely possible, depending on what the 9th Circuit says," said ABC News Supreme Court contributor Kate Shaw. "If the 9th Circuit just finds that the TRO was too broad, I don't think there's anything preventing Robart from entering a narrower injunction. On the other hand, if the 9th Circuit says very definitively that the balance of hardships tips in favor of the federal government, that would be a lot harder to get around."
Could the TRO Be Left in Place but Modified by the Appellate Court?
Flentje asserted that the TRO entered by Robart is overly broad and that the plaintiff states have no standing to challenge the president's authority to enforce provisions of the order affecting refugees and visa holders who have never before been admitted to the United States. He suggested that if the temporary restraining order remains in place, the appellate judges should modify it to apply only to "previously admitted aliens who are temporarily abroad now or who wish to travel and return to the United States in the future," he said.
Purcell countered that limiting the restraining order in that way "would not remedy the [executive] order's violation" of the First Amendment's establishment clause "by favoring one religious group over another" — which the plaintiffs contend renders the executive order illegal on its face.
Asking the appellate judges to modify the TRO in a way that could significantly affect the enforcement of certain provisions of the executive order, Shaw said, is "something I can't see the judges getting very enthusiastic about," in part because of the confusing rollout of the order.
In the first few days after Trump signed the executive order, there was extensive confusion about its application to legal permanent residents of the United States who hailed from the affected countries. In a memo to federal agencies sent five days after the order was signed, White House counsel Don McGahn acknowledged the "reasonable uncertainty" about whether the order was intended to apply to legal residents of the United States and clarified that it did not.
"Asking [the appellate judges] to impose another set of limiting conditions atop this White House counsel memo, which already limits the executive order," Shaw said, "just from a practical implementation perspective, is not realistic, especially considering the chaos we have already seen, even when there was just the executive order in effect."