It's worth saying that expanding the VA isn't as easy as allowing more folks to sign up. The VA isn't an insurance system, where you can just give folks a card and they can start accessing its awesome care. The VA is a self-contained health system: It owns its own hospitals, employs its own doctors, buys its own technology. To radically increase enrollment would require building a lot more infrastructure, buying a lot medical machinery, hiring many more doctors and nurses. That's not to say it couldn't, or shouldn't, be done, but unlike letting people buy into Medicare, scaling the VA up to absorb new populations would cost money and take time.
Update: It occurs to me that I should make explicit that doing so would be a good thing. More VA facilities, a larger VA program, and maybe an eventual transformation into a national service would all put a smile on my face.