Are our "unalienable" rights only those which are enumerated in the Constitution?
No. They are those granted to us by G-d. They are self-existent, not created by the whim of the majority.
Of course, absent a new Moses, it is always difficult to determine what G-d hath said in specific situations. That is why our Republic requires persuasion, debate, and vote for representatives who then vote on issues.
But our Republic was meant to govern those who had internal morality, and a specific internal morality which even the Deist Jefferson recognized as "eternally true." The experiment will fail if we become a nation who believes that everything is equally true and the only thing that matters is the whim of the majority.
Shalom.