Don't mistake the US political system for a European style party system. The 1920s - 30s Oklahoma cowboy humorist, Will Rogers, put it well when he said, "I'm not a member of an organized political party, I'm a Democrat!" While our political parties are the single best predictors of how our Congressmen and Senators vote, the correlation is far from perfect. When Senator Arlen Spector changed parties from Republican to Democrat his new party was well aware that he would vote against them whenever he chose to do so - unlike when Winston Churchill crossed the aisle to become a Conservative again after many years as a Liberal.
Remember too, that there is as much battle between the institutions of government - Pres v Congress - as between the parties. Mr Obama has appointed a couple of Republicans to his Cabinet - most prominent is SECDEF Bob Gates - as his predecessor had appointed at least one Democrat. American policies are not party policies, although party preferences do have an effect on shaping them. They are the product of institutional and personal experiences, education, and training tempered somewhat by party.
So, the American military responds to its political masters far more on an institutional basis than on a party basis. Moreover, by our law - the National Security Act of 1947 as amended - and through 62 years of practice, the American military in the form of the CJCS is very much involved in the deliberations that establish Presidential policy. While the CJCS is a "statutory advisor" to the Pres, SECDEF, and the NSC, he is a full member of the policymaking Principals Committtee, the VCJCS is a full member of the Deputies Committee, and Joint Staff officers are full members of the intergency working groups/committees (by whatever name they currently have) that make defense and foreign policy under the NSC.
In short, our system is unlike that of the UK, any other English speaking democracy, or that of Israel, or any other country for that matter. Indeed, our process is simply messier than most others.

Cheers

JohnT