If I'm your lawyer, and you win, and the other party seeks an appeal to the Supreme Court, that's exactly what I write for you. Because it's not my job to insert my judgment about whether I think the Supreme Court should hear the case, my job is only to argue in favor of the interpretation that lets you win the quickest.
In the context of Constitutional challenges to Congressional laws, the DOJ has the same job. They will first seek to have review denied because that's the quickest way for Congress to win. If review is granted, the Solicitor General, whose office is part of the DOJ, will have to drag his ass to the Supreme Court and argue strenuously in favor of upholding the Constitutionality of Congress's law.
That's just the way the adversarial legal system works.
Also, your Due Process point is way out of bounds. Due Process does not entail the right to Supreme Court review. The Supreme Court could deny the petition for no other reason than "it sounded boring" and there would be no Due Process violation.