The Supreme Court term ends next week. But its biggest case of the year just arrived.

The Supreme Court’s nine justices will decide the fate of President Trump’s “travel ban” — the executive order that’s been put on hold since its introduction in March, and which is descended from an earlier policy that inspired massive protests at airports around the country during the first week of his presidency. On Thursday, during its last closed-door conference meeting of the year, the court will decide how it’s going to decide that fate.

The court will take up the question of what do to with the lawsuits against the executive order, which has been blocked from going into effect by court rulings issued a day before it was scheduled to go into effect in mid-March.

Their decision will determine the course of immigration policy for the next several months — or longer.

And their options range from handing the administration a stunning and unprecedented victory, to giving it a quiet and ignominious defeat.

The Trump administration wants a decision as soon as possible. Obviously, they’re displeased with the lower courts’ rulings — which are, cumulatively, the kind of pummeling you’re more likely to see in a Road Runner cartoon, with the administration playing Wile E. Coyote — and hope to see them pushed aside.

But they may also be worried that the longer the travel ban is kept on hold, the weaker the argument for putting it in place at all is — especially if the administration has all summer to conduct the review of current visa “vetting” procedures that was supposed to be the justification for the travel ban to begin with.

The fight over the travel ban is exactly the sort of high-profile, politicized battle that’s characterized the Supreme Court in recent years. In theory, it’s not supposed to rule on “political questions”; in practice, the biggest policy decisions made by the federal government have a way of turning into constitutional issues. How the Supreme Court feels about the ban itself isn’t yet clear, or even relevant. The question is how it feels about its own role in the fight over the ban — and whether that leads the justices to try to get the case over with, or to proceed with deliberate caution.

The last day of the Supreme Court term — when it will release its last decisions and court orders before recessing for the summer — is Monday, June 26. But the crucial date in the travel ban cases is this Thursday, June 22nd.

By that point, the justices will have received all the briefs it’s asked for: from the federal government arguing for the travel ban to be put in place; from the advocacy groups who successfully put it on hold on the East Coast, in the Fourth Circuit case IRAP v. Trump (which is the case the justices are formally considering whether to hear), and from the states that successfully challenged the travel ban in the West Coast case Hawaii v. Trump (which the Supreme Court has asked for briefings on as well, indicating they’ll probably roll the two cases together); from supporters of the travel ban urging the Supreme Court to take up the cases, and opponents urging them to let the lower-court rulings stand and keep the ban on hold indefinitely.

That’s when the justices will meet, behind closed doors, to decide which cases they’re going to take on — and when they’re going to hear them. It’ll be the justices’ first chance to formally look at the travel-ban cases.

If the court wants to resolve the travel-ban cases at any time in the next several months, it’s going to have to agree to a schedule on Thursday.

The Supreme Court doesn’t tend to rush itself to put cases on the calendar. Traditionally, the cases it agrees to hear at the end of the term get put on the calendar for the following fall. And in recent years, the court hasn’t even made the decision about whether or not to hear a case immediately — they’ve often allowed a case (especially a major case) to hang around on the agenda for two or more conference meetings before voting on whether to grant certiorari.

They don’t have that luxury this time. If they aren’t ready to agree on a path forward by the end of Thursday’s meeting — unless they extend the term just to continue thinking about the travel ban cases — they won’t have another chance until the fall.

Given that the administration is hoping to have the travel ban in place over the summer (it even asked the Supreme Court to put all the lower-court rulings against the ban on hold while the justices look at the case), that would be an unfortunate development indeed.

Typically, justices have two options when a case is appealed to the Supreme Court: grant certiorari and agree to hear the appeal, or deny certiorari and let the lower court ruling(s) stand. As long as at least four justices agree with the first option, the case is put on the docket.

But nothing in the travel-ban cases has been procedurally straightforward, and the fact that we’re coming up on the court’s summer recess has added additional wrinkles. So there are essentially five different scenarios that could come out of Thursday’s conference: four options the justices can decide to take, and what happens if they can’t make a decision at all.

Here are the scenarios from least likely to most likely:

Any of these is theoretically possible. But not all of them are equally likely.

Because this is such a high-profile case, it’s likely that the Supreme Court will want to have a say — which means they’re unlikely to simply decide not to take it up (and let the lower court rulings stand), and reduces the odds that they won’t be able to come to an agreement at all on Thursday about what to do with the case (and will allow it to sit on the table over the recess).

The court’s respect for the traditional judicial process, on the other hand, is likely to make them less-than-receptive to the Trump administration’s request to push aside the lower court rulings and let the travel ban go into effect over the summer.

If the court doesn’t give the Trump administration what it wants on the travel ban immediately, though, it might be more likely to postpone its own vacation to resolve the case at the Supreme Court level as quickly as possible — thus avoiding the risk of letting the travel ban remain on hold for months, then ruling in the fall that it really shouldn’t have been put on hold to begin with.

Ultimately, it’s worth remembering, the Supreme Court is more likely to side with the administration and uphold the travel ban than the lower courts were. Critics of the travel ban deliberately picked liberal-leaning circuit courts to take up the case, while the Supreme Court, especially with the addition of Trump nominee Neil Gorsuch, has 4 reliable conservatives and one swing vote.

What the justices decide in how to take up the case probably won’t tell us much about how they’ll ultimately rule. (The exception is if they grant the Trump administration’s request to put the travel ban in place over the summer; if five justices believe that the ban should be in effect immediately, they probably believe that it’s constitutional and the lower courts were wrong.)

But the attention being paid to whether, and when, the justices take the travel-ban cases up is likely to remind them of just how high-profile this case is — and of the concerns it’s raised among progressives about the independence of the judiciary, and among conservatives about the relationship between campaign rhetoric and policy.

Above all, it’s a reminder that at the end of the day, only the Supreme Court will be able to put this legal battle to bed. The question is not whether they do so, but when.