On September 24, the Solicitor General sought an emergency stay, as well as an administrative stay, of the Boston District Court's order blocking third-country removals. Justice Jackson promptly issued a schedule with the briefs due on September 28, but did not grant an administrative stay. The Solicitor General, perhaps anticipating this denial, preemptively asked that the denied application should be referred to the full Court. At the time, I speculated that by virtue of Jackson's denial of the administrative stay, the case was effectively referred to the full court.
Another theory a colleague suggested is that the Justices had already discussed the case, and the four-day briefing schedule was something of a compromise. That is, Jackson could have given a week or longer, but that delay would have triggered an administrative stay. To avoid that outcome, Jackson agreed to a shorter briefing schedule. I suppose that's possible, but if Jackson was unwilling to vote for a stay, and knew there were five votes for a stay, what exactly would that compromise buy?
In any event, the Court did not wait for Justice Jackson to formally refer the case to the Court. On September 29 around 2:40 ET, the government filed its reply brief. About 40 minutes later, the Court issued a very detailed order granting a stay, treating the application as a cert petition, granting that petition, and setting the case for argument in December. The Court also requested briefing on at least three specific questions presented: