If you want to argue that the VA's problems are a sign of what happens under true government control of a health care system, well, there's an argument to be made there. Some of the problems at the VA — namely, long waits to see certain doctors — are similar to the biggest complaints about other socialized or quasi-socialized health care systems, including the UK's.
The VA is about as socialized as it gets: The government owns the hospitals, employs the doctors, and finances the coverage.
And the VA is about as socialized as it gets: The federal government owns the hospitals, employs the doctors who work in those hospitals, and finances the coverage that veterans use to get care.
Obamacare, though, is not socialized medicine. It's not a government takeover of the health care system. Sure, people call it that, and in comparison with charges like "death panels," those characterizations don't sound so off-the-reservation. But they're still wrong.
Most people accessing the health care system through Obamacare will do so by purchasing private insurance through the law's exchanges. The federal government regulates those insurance policies and requires them to cover certain services. The vast majority of exchange customers also receive subsidies, funded by the government in the form of tax credits, to help pay for their premiums. So it's not like the government isn't involved at all.
But, unlike with the VA, no one on the exchanges is buying insurance from the government; it's all private coverage. The government doesn't decide how much that coverage costs. It doesn't employ doctors, or decide how much they'll get paid, or require them to accept any of the insurance plans sold through the exchanges. "Obamacare" is not a health care system. The VA is.
Obamacare also expands eligibility for Medicaid, which is a government-run program. But it's still not socialized medicine like the VA: You don't use your Medicaid card to go to the Medicaid hospital for an appointment with the Medicaid doctor, the way veterans do with their VA coverage.
"If the GOP can't find the courage to enact fundamental reforms of the VA, it has no right to complain about Obamacare," conservative health care expert Avik Roy wrote in a blog post that suggests moving veterans into Obamacare's exchanges.
The structure within the VA that allowed long backlogs to develop and, allegedly, allowed workers to create secret, off-the-books waiting lists, is a structure that has a lot to do with the specifics of that system.
Private insurance doesn't create backwards incentives to trap patients in an endless appeals process, the way the VA apparently does. Plans sold through the exchanges offer different levels of benefits and different networks of doctors; the VA is the VA. The VA is a unique system with specific flaws. Its problems don't simply photocopy themselves onto the private insurance market just because they're both health care systems.