Conor Friedersdorf tries to reconcile the disconnect and asks what liberals would do if they reject Paul. Conor always has smart things to say. And that is the case in this instance.
But one thing missing from his article and all of Glenn Greenwald's on this subject is the effect of the economy on the public's attention. The media and politicians help drive political narratives. And since the recession towards the end of 2008, that narrative has largely been focussed on the economy.
Thus, because of the media coverage and because the economy affects them more than Iraq/Afghanistan/executive power/etc., the public has been more focussed on that issue more than everything else. These issues were so important in 2006 and most of 2008 because the economy was doing well. The media and the public were able to focus their attention to other issues. And aside from a bad economy, wars are usually big news.
I'm not sure if there is polling that addresses these issues that Paul is supposedly challenging liberals on. But I don't think there would be huge differences in liberals' opinions now as compared to 06 and 08. There probably will be some differences if you frame it in a manner that has Obama or a liberal supporting or implementing the anti-libertarian policy because confirmation bias can be strong. But I think part of the disconnect with Paul and liberals is a lack of focus on the national security/foreign policy issues and the continuing focus on a crappy economy.