To my knowledge, there are no current polls about military preferences for the GOP candidates. There are a few unscientific polls done by a newspaper, The Military Times, that measure military approval of the president, but that is it. They show approval for president Obama within the military at around 25%.
I have done some research in this field, however [paper available here]. One of the main take-aways from my research is that Republican officers in the military and elite veterans are no different, on average, than Republican civilian elites once we control for demographic factors. Although my work focuses on senior officers and veterans, Jason Dempsey’s book, Our Army, and Jeremy Tiegen’s paper support this general claim for soldiers and veterans, respectively.
I find one exception, however: military officers are marginally more conservative than civilian Republicans on social issues. This may bode well for Santorum v. Romney, but there is no evidence suggesting that any GOP nominee would have trouble winning the ‘military vote’ since there really is no such thing. There are not many Democrats in the military and there are even fewer liberals in the ranks; in general, most Democrats in the military are moderate or conservative Democrats (especially in the higher ranks).
There is one other small point to note. Although Ron Paul’s campaign has claimed to have the overwhelming support of military personnel over the last few months, there is not much evidence to support that view at this point. The last time I checked on the FEC database, around 500 military folks (active duty and retired) had contributed a little over $100,000 to Paul’s campaign, out of approximately 22 million veterans and 1.5 million service members. Paul has, in fact, received more contributions from people associated with the military than have other GOP candidates, but those contributors are not necessarily representative of the military as a whole. The low levels of participation among members of the military seen here also is consistent with the research of my colleague here at West Point, Heidi Urben, who finds that – with the exception of voting – members of the Army participate in domestic politics at very low rates.