The Congress shall have Power ... To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries;
I don't buy it. I think it is correct to say that Congress's constitutional purpose and authority in passing copyright law is based on the public good, and not a natural right theory. But it could also be true that Jefferson and the other Founders believed in the natural rights theory for copyrights. That is because Congress has limited powers, and they did not expect Congress to address every natural right that people have.
But the Constitution's wording seems carefully chosen to allow for the natural rights view. If it really wanted to reject the natural rights view, it could have said:
The Congress shall have Power ... To promote the Progress of Science and useful Arts, by granting for limited Times to Authors and Inventors exclusive protection for respective Writings and Discoveries;
Instead, the Constitution refers to the copyright/patent as a Right, refers to their writings as if the writings are owned by the author before Congress even gets involved, and give Congress the power to secure the right rather than grant the right.
If the copyright is limited to promoting progress, then I think that the US Supreme Court should strike down the copyright term extension, as nobody seriously thinks that it promotes progress. See Eldred v. Ashcroft.