There is a fairly active literature on attitudes of military personnel. The bulk of the literature has come out of sociology, much of it inspired by the pioneering work of Morris Janowitz (Chicago) and Charles Moskos (Northwestern, passed away in 2008). The primary academic journal in the field is Armed Forces and Society.
Political science engagement has been primarily driven be interests in the “civil military gap” that has grown as a consequence of the all-volunteer force. Peter Feaver, an old friend and colleague of mine when at Duke, has been a leader in this area, working mainly through the Triangle Institute for Security Studies, along with Dick Kohn (History at UNC, now emeritus) and Chris Gelpi (Duke, moving now to the Mershon Center at OSU). I worked with Peter, Chris, and Dick on a set of parallel surveys of civilian and military elites and the mass public, and much of this work was published in a 2001 MIT Press book Soldiers and Civilians: The Civil-Military Gap and American National Security.
Some of the ideological and partisan information that Josh asked about is contained in that book, and Dempsey’s work is a superb addition to the field, in some ways updating the TISS surveys, and in other ways challenging some of our conclusions. I think there remains some really interesting questions, not only about the partisan and ideological leanings of the military, but other questions, such as how service in the military may interact with, or even offset, some demographic influences on voting turnout and voting behavior.
From a methodological perspective, there are a number of challenges to answering Josh’s question. The military population can be devilishly hard to track. Of course, the Pentagon knows who are enlisted personnel, but is not about to allow anyone to randomly sample off of that list, and even if they did, are likely to resist including a lot of politically charged questions. If you choose to work outside of the Pentagon, you face other hurdles. A typical national survey will include a very small number of self-identified military personnel, misses anyone who lives on base (if I recall correctly, the NES sampling scheme does not include on-base housing), and anyone serving overseas. If you think you can sample from voter registration lists, think again. While in the ideal world, all military personnel will have an FPO or APO address, many who live off base may not.
One last data source that readers may be interested in is the Federal Voting Assistance Program’s biennial survey. There is not a lot of ideological and partisan information, but there is a lot of demographic information. The surveys are available at this website.