The case may go to the US Supreme Court on the issue of the imposition of the temporary stopping of Trump's ban until a hearing on the constitutionality and legality of the ban at the District court level. But the case may be sent back to the District Court for action on the merits of the case against the ban. It is possible that the Supreme Court will say enough about the constitutionality issue to offer strong guidance on the law to the district court(s), but the hearings at the district courts where the challenges to the law are heard will decide the merits of the case against the ban. If the government loses, there could be another appeal to the Circuit Court of Appeals and then another appeal to the US Supreme Court as well.