OK, it's been a few years since I've been dealt with this issue, but I'll take a stab:
DOD medicine and VA medicine are really two completely separate issues. The DOD healthcare system primarily serves active-duty military members, their dependents, as well as military retirees (those who retired from the military after serving 20 or more years, and those who were medically discharged from the service for serious injuries incurred while on active duty)
This system is known as Tricare and falls under the auspices of the Department of Defense and the Secretary of Defense (Rumsfeld at the time of the last election), who works for the President
The VA is part of the Veterans Health Administration, which is part of the Department of Veterans Affairs, headed by Secretary of Veterans Affairs, another cabinet level post appointed by and answereing to the President. The VA serves veterans (those who have served in the military for any length of time). Eligibility for VA healthcare depends upon several factors, including whether or not the veteran receives VA benefits for an injury or illness that is deemed "service-related" (e.g. certain types of cancer which may emerge decades after their military service ended and is considered to have been caused or exaggerated by some exposure they encountered during their military service, like agent orange), and the income level of that veteran. There are other factors that go into this determination, but you'd have to talk to a bureaucrat for that.
I think that the controversy to which you're referring was related to eligibility for VA healthcare. To determine eligibility, a veteran is classified into a priority group. A high priority group would include a veteran who receives disability compensation for an injury he/she received in the service. A low priority group would include a vet who has no service related injuries or illnesses, and is able to afford his own health insurance. Every year the secretary of Veterans Affairs must decide where to put the cut-off for enrollment in VA healthcare. Circa 2004, there was a temporary freeze in new enrollments for certain lower priority groups because there simply was not enough alllocated to VA to fund new enrollments. While the president and congress wouldn't hesitate to tell you that they actually raised gross funding for VA, what they don't mention is that when factored against inflation, rising costs, and new enrollments, the funding for VA was a net decrease. Thus the freeze in new enrollments. Understandably, many veterans were upset, as a lot of vets view access to VA healthcare as a right that they earned by serving their country.
At the time, we had a Republican president and a Republican-controlled congress in both houses, so take from that what you will, but the fact that Defense and VA are two separate cabinet-level postings under the president illustrates how support and funding for one does not necessarily translate to support for the other
THis poem sums it up a lot more eloquently than I ever could:
God and the soldier
All men adore
In time of trouble,
And no more;
For when war is over
And all things righted,
God is neglected -
The old soldier slighted.
-Anonymous