The Common Core is not a national curriculum, because it is not a curriculum at all. It is only a set of standards, and that's completely different from the scope and sequence of curriculum planning. But like that terrible Match.com date you went on, the standards/curriculum distinction only looks good on paper.
Federal laws clearly give us the right as parents to guide the education of our children. While the Secretary of Education has recently pushed for changes to those laws in order to give corporations as much access to your child's data as any teacher or administrator has, he hasn't been able to take away our right to decide what's best for our child. Not yet anyway.