Right now State of Washington v. Trump is, as I understand it, still a district-level case. Judge Robart issued a TRO against the order, and the DoJ appealed for a stay on the TRO. The district court has not yet gotten to the point of issuing a preliminary injunction.
So now that the 9th Circuit has denied the request for an emergency stay on the TRO, can they really take this to the Supreme Court just for the sake of an emergency stay?
Secondary question: say the answer is yes, and they do, and then the Supreme Court makes a decision. Doesn’t it only affect the TRO? The district court can still go on to issue its final decision, and even if it’s in line with SCOTUS as it must be, then surely the losing side can appeal that to the 9th circuit and then do we go back to SCOTUS a second time for the final ruling? Seems ridiculous.
How would this all work?
The decision can be appealed to the Supreme Court, though SCOTUS may decline to hear the case (for example, on the grounds that the issue would be moot, that it isn’t really an emergency, or that it would be a 4-4 waste of time). Or they might grant cert (as ohwilleke points out, it goes to Justice Kennedy and I agree with their bet that he would have granted cert. though now we know it’s not going to go to SCOTUS), let it be heard, and rule unanimously (highly unlikely, though). If there is a fundamental issue identified by the case, then in principle that could have consequences way beyond just granting overturning the TRO, though again that’s unlikely.
They might make a ruling about the nature of unappealable TROs vs. appealable temporary injunctions (the appeals court found that although it was called a temporary restraining order, it found that ‘the district court’s order possesses the qualities of an appealable preliminary injunction’ – ‘Ordinarily, temporary restraining orders, in contrast to preliminary injunctions, are not appealable’, Bennett v. Medtronic, 285 F.3d 801. and citations therein). There are plenty of big issues in the ruling especially about due process and establishment.