The speaker of the house herself affirmed recently that the president does not have the constitutional power to do this, and the court will likely agree. The president is using 9/11 educational legislation signed by Bush that focused on military and disaster victims for this blanket debt cancelation. It is a dramatic expansion of power that was never intended.
However, the court cannot consider the question unless someone can show actual harm by the president's action, and thus prove standing.
That standing may be denied in the trial court, but after a raft of appeals, SCOTUS may grant standing and remand. Then the trial begins, and we will have another set of appeals before us (and perhaps an injunction) when the trial concludes.
It will be a long and bitter road, strewn with disappointment, either way.