The argument from Jindal amounts to a syllogism. If the federal government funds the tests, and the tests control what teachers do in classrooms, the governor claims, then the federal government is controlling curriculum, which is illegal. Jindal says the arguments from common-core and PARCC supporters about the damage uncertainty over testing creates for teachers prove his point.
Whether or not the common standards lead to the establishment of common curriculum is the question to answer. For any moves by the federal government that direct or control school curriculum are clearly outlawed by at least three separate pieces of federal legislation. While curriculum in language arts changes based on the novels and the writing assignments, the role of standards in driving curriculum in the math and sciences is more obvious. And, as Gov. Jindal notes, if the test requires learning in a specific manner in order to succeed on a test that is funded by and basically required by the federal government, then that very action is dangerously close to violating laws on curriculum.
While I am not sure if the CCSS represent a federal takeover scheme, I am a little suspicious of attempts by Core proponents to differentiate the standards from the necessarily similar curriculum. Of course, this discrepancy is the problem when people outside of education try to make policy.