The Plaintiffs' suit was rejected in federal district court in Maine, which was then affirmed by a unanimous panel of judges on the First Circuit. The plaintiffs then applied to the Supreme Court for emergency relief, asking for the court to grant them an injunction against the law taking effect while the court decided whether to hear their case. In their concurrence, Justice Kavanaugh and Barrett specifically signaled that they were planting a marker regarding perceived abuse of the court's "shadow docket" and left open that they might still be willing to vote to hear the case with the benefit of "full briefing and oral argument," but that they were unwilling to grant the injunction the plaintiffs asked for in the meantime.
When combined with the votes of the three dissenting justices, it seems that at least five justices are potentially willing to hear the case, if presented to them in the correct procedural posture. In order for a case to be heard by the Supreme Court, only four justices need to agree to grant a writ of certiorari.
Writing for the dissent, Justice Gorsuch noted that he would have granted the immediate relief sought by the plaintiffs, noting, "with Maine's new rule coming into effect, one of the applicants has already lost her job for refusing to betray her faith; another risks the imminent loss of his medical practice. The applicants ask us to enjoin further enforcement of Maine's new rule as to them, at least until we can decide whether to accept their petition for certiorari. I would grant that relief."
Although the court may eventually overturn Maine's mandate, the fact that they refused to grant the plaintiff's application for temporary injunction means that the law will be permitted to go into effect, for now, which means that healthcare workers will be required to get the vaccine or lose their jobs, at least until the court eventually hears the case and rules on it.