Consider the Lawrence case decided by the Supreme Court in June. The Court determined that Texas had no right to establish its own standards for private sexual conduct, because gay sodomy is somehow protected under the 14th amendment “right to privacy.” Ridiculous as sodomy laws may be, there clearly is no right to privacy nor sodomy found anywhere in the Constitution. There are, however, states’ rights—rights plainly affirmed in the Ninth and Tenth amendments. Under those amendments, the State of Texas has the right to decide for itself how to regulate social matters like sex, using its own local standards. But rather than applying the real Constitution and declining jurisdiction over a properly state matter, the Court decided to apply the imaginary Constitution and impose its vision on the people of Texas.
Outside of a perhaps small group of libertarians, libertarians were pleased with the Lawrence decision. Rep. Paul's comments reflect the mindset of the "New Deal Jurisprude", who believes that unenumerated liberties should be determined via democratic process rather than vigorously protected against the passions of democratic factions. On that note, he sounds more like a judicial conservative, echoing similar sentiments heard amongst conservatives when the Lawrence decision was handed down.
Moreso, I do not read the Ninth and Tenth Amendments the way Rep Paul does. The Tenth Amendment states, clearly, that those powers specifically not granted to the federal government are reserved to the states or to the people. From this, we can draw two conclusions: 1) the amendment itself is a reaffirmation of the pre-existing constitutional structure. It adds nothing that can not be derived from the original Constitution. 2) the Tenth Amendment recognizes additional powers that fall to local responsibility but in no way makes any determination as to what those powers are or what those powers are not. In other words, the Bill of Rights does not define the proper role of the state police power (although, properly interpreted, it establishes firm constraints with respect to the Privileges or Immunities and the Due Process clauses of the 14th Amendment). It may begin the discussion, but it does not end it.
Also, if the Ninth Amendment suggests that individual unenumerated rights are to be protected in the same fashion as enumerated rights, what pray-tell does this have to do with states rights? Furthermore, as the Ninth Amendement describes individual rights and the Tenth Amendment describes power, why conflate the two?
I know there is some scholarly research that addresses this (i.e. the Ninth Amendment debates between Randy Barnett and Kurt Lash), and, although I may have a passing knowledge of the issues, I am not up to speed on all of the arguments. However, that is basically irrelevant. This is not a debate about the proper way to interpret the Constitution (I do not ignore the possibility that my view of things could be - or have been - proven to be different than how I understand them to be). To me, he is more Robert Bork than Randy Barnett, and no right-minded libertarian subscribes to Bork's (or Paul's) pandering to democratic majorities at any level of government. Libertarians know better.
Now, why do people refer to him as a libertarian? I agree with Sandefur that he his more akin to a paleoconservative.
Hat tip to Tim, although I think that his link "II" at the bottom of his post is a duplicate of "I". I'd really love to read that Part II. :)