Well, it depends. Reagan to me is easy to get caught up in the labeling process, but I would immediately caution against labeling him either: 1) Libertarian 2) Neoconservative (as both groups blindly try to claim him, cherry picking some things, but conveniently ignoring other things). Most of the time, the first generation (most of the time, domestic social policy or intellectual thought, but a decent chunk were also foreign policy specialists or identified themselves as more concerned about that) either rejected the label or were indifferent toward it. Later, some could actually subscribe some identity toward it and would reflect upon that. Now, the word neocon, has either been "meaningless" or a "badge of honor" to those so-labeled. To some labeled as such, the mere act of agreeing with the Iraq war was proof positive of being a neocon (hence why some thought the label meaningless). However, in these post-Bush times, it once again (like the term's entire history it seems) becomes problematic to figure such a thing out, but I'll try.
I would say with Obama, much of the identity process is not there yet with him (or at least as much as we know). While he may agree with some instances here or there of the "neoconservative creed" (in this instance, foreign policy notion of democracy promotion and muscled foreign policy interventionism), I believe Obama is far from a person who would truly feel that way. To me, Obama neither resembles the simplistic joke that a "neoconservative is a liberal mugged by reality" (the statement by Irving Kristol was a play on someone else's statement, for everyone's information) nor a person who actually believes in either 1) immense "Jihad hunting" like some 2) Pax Americana democracy promotion by force if necessary. It is more than likely that Obama is neither a believer of domestic policy neoconservatism (which somewhat typically is more skeptical of some of his endeavors thus far....save for portions of Obamacare which theoretically could be somewhat popular with some "neoconservatives") nor a subscriber to the notion that folks like Kristol, Perle, Wolfowitz and so on had much he could agree with.
With Kristol & Kagan, there was a particular brand of "neoconservatism" (though in all actuality, the two coined it "Neo-Reaganite" and merely gave into the term neoconservative) that was to be spread: American Hegemony in a post-Cold War era that required American vigilance in the face of newer threats like North Korea, Iran, Iraq, and so on. Terrorism was sort of there, sort of not there, but basically, the new threats emerged in such a time like the 1990s that these guys were thinking that it needed to be dealt with uniquely and more strongly than most of the foreign policy apparatus around it.
This then gets conflated with the whole "concerned for the fate of Israel" bit of, say, Commentary Magazine, and so on. So, some will emphasize some aspects of democracy promotion, while others will be thinking about being vigilant militarily and diplomatically against agents of terrorism-fearful of blind interventionism just because it promotes democracy (which does not necessarily mean the ends they desire).
This brings into question the whole term neoconservative, just like many times before. So in many instances, I will respect many so-labeled, but dismiss others labeled (like Rumsfeld and Cheney, whom have long been considered merely conservative foreign policy hawks from the get-go).
