Sure, Sen. Rand Paul (R-Ky.) has gone out of his way to call himself a constitutionalist conservative rather than a libertarian per se, and many (perhaps most) libertarians object to his objections to abortion (though if you genuinely believe a fetus is a human life, there is nothing inherently unlibertarian about laws to protect them).
to eliminate mandatory minimum sentences for pot possession. He wants to carve a compromise immigration plan with an “eventual path” to citizenship for illegal immigrants, a proposal he believes could be palatable to conservatives. And he believes his ideas — along with pushing for less U.S. military intervention in conflicts overseas — could help the GOP broaden its tent...
Sure, on immigration he is a guy who as candidate called for an underground electric border fence and as Senator has introduced bills to kill birthright citizenship. These are stances that culturally don't tend to go along with trying to find a sensible path to legality for those already here.
But there is nothing ideologically contradictory about it either. Rand will doubtless not, like his dad Ron Paul did in 1983, enter into the Congressional Record lines (from Austrian economics teacher Hans Sennholz) such as:
In the cause of individual freedom, we must defend the rights of all people, including illegal aliens. But if the political rights of American citizenship entail the denial of the human right to work diligently for one’s economic existence, and if we are forced to choose between the two, we must opt for the latter. The right to sustain one’s life through personal effort and industry is a basic human right that precedes and exceeds all political rights.
Still, one can be against letting in more immigrants or letting their kids become citizens without also being an advocate of deportation or even "self-deportation." (Of course, it is disappointing that Rand's libertarian leanings don't allow him to see that even treating immigration as a big issue/problem at all isn't necessary.)
The Politico article goes on to explain that Rand is still being cagey about his 2016 presidential plans (my own read of the Paul world gives a very, very, very strong probability to his running) and that being an ideological outlier in the Senate makes it hard to actually get your agenda through.
It is alas not unusual for non-conservative media to treat "Tea Party" as meaning "everything liberals don't like about the GOP turned up to 11" rather than understand their distinct qualities. My colleague Nick Gillespie points out to me this morning that NPR persists in referring to defeated Missouri Senate candidate Todd Akin as a "Tea Party" candidate despite how such Tea-Party identified groups as FreedomWorks fought against him in the primaries for being just one more big-government Republican.
The Tea Party idea at its best is about cutting government spending to manageable levels, which Paul has been great about. Libertarian approaches to drugs, foreign policy, and immigration are necessary parts of that. Other right-wingers have long recognized the sinister libertarian dangers of Tea Party man Rand Paul.
Reason's June 2011 cover story on Rand Paul.