Understand what's at stake here, because it's a lot more than the implementation of one policy. What the administration is asserting here is exactly what they should be - that the lower courts should not be mindreading the president's intentions based on statements on the campaign trail or anything else. If his action is legal and he has the authority to take it, that's it, full stop. Game over. Whatever you might think he really wants to do is irrelevant.
It seems almost inconceivable to me that SCOTUS doesn't deliver at least five votes affirming that argument. It ought to deliver nine.
But the first step was in asking them, and that has now happened: