Yup. That's pretty much how it worked.
Alice Rivlin, senior fellow in the economic studies program at the Brookings Institution,
doesn't get the conservative myopia about just what it was that they got in Obamacare.
In general, Republicans argued that relying on market forces would give people what they wanted while also putting pressure on the health system to offer more effective care for less money. They argued for subsidizing Health Savings Accounts combined with high-deductible (catastrophic) insurance. Their theory was that, if consumers were spending their own money for normal medical expenses, they would demand information on providers’ prices and success rates. Providers would respond by offering better care for less. Some Republicans advocated turning Medicare, with its fixed benefits and prices, into a premium support plan in which the government would pay a fixed subsidy (sometimes called a voucher) and consumers would choose among private health plans, shopping for the best deal. They believed competition would raise the quality of care and hold down costs.
Democrats took that premise—"relying on market forces would give people what they wanted while also putting pressure on the health system to offer more effective care for less money"—rather than pushing a single-payer solution that would have truly provided universal health care. They layered on to it the regulations necessary to make it actually work and made it far less punitive than what Republicans asked for, but they got it done. And the results? A slowdown in the increase in healthcare spending, much more competition in the marketplaces, and millions of people with coverage they want.
Rivlin isn't actually dumbfounded that Republicans aren't applauding getting most of what they've always said they wanted as a result of healthcare reform, but she does do a good job of pointing out that their free-market arguments are bunk.