There are a handful of reasons Obamacare
could work, the most compelling being that once it's established and people are getting their insurance through it, most of them won't even think about the fact that it's Obamacare. It'll just be their health insurance.
Beyond that, the worst-case scenario for Republicans is the mounting evidence that the critical 18-34 demographic is likely to participate. Republicans don't want that, because younger healthier people paying into the system will boost the older and sicker people insurance companies will now have to accept. That means premiums can be kept at a relatively affordable rate for everyone, and costs can generally be kept down.
Those people are likely to sign up if they hear about the opportunity, and that's what the administration has focused on making happen, with an assist from private insurers who see a great opportunity for a bunch of new customers. The administration is using the same model for targeting critical groups for outreach as the Obama campaign, which makes sense. They're trying to reach the same populations.
There's a model for this working: Massachusetts, the state with the lowest rate of uninsured residents in the country. The difference, of course, is that there wasn't an entire political industry created around making Romneycare fail in Massachusetts. But an existing successful model argues that once Obamacare gets over the initial hurdles and starts taking hold, it will fade in people's minds as a contentious political fight and just be a normal, everyday thing.
That's the strongest factor in its favor, and why Republicans are so anxious to find anything to make it stop. Because the stuff that's in there, people like it. Even Kentuckians who hate Obamacare like the stuff that's in it. At a certain point, they're going to forget all about the fact that it's that law, and just enjoy the fact that they have insurance that can't be capriciously taken away. Once that's established, we can move on to the idea that government being involved in health insurance isn't such a bad thing, and start work on health care reform.