If you take God the Creator out of the Constitution as the anti-Constitutionalists battle to accomplish, you also might imply that our rights and freedoms as defined in the Declaration of Independence are not endowed as our natural birthright from God.
This leaves us as "subjects" of the Government who instead fill the role as our ruler, and benefactor of bestowed right and freedoms. We'd have fought a revolution for naught.
It's really not so hard to see the end game of the anti-Constitutionalists and their "useful idiots" who don't see the forest for the trees" when it comes to erasing God from the documents of our nation's founding.