Of all the stories critics have used to scare people off of health care reform (bureaucrats will choose your doctor, death panelists will snuff your granny), the one about rising costs may be the most tenacious. “Consumers will have fewer choices and pay much higher premiums for their health insurance,” Ohio Lt. Governor Mary Taylor declared last month, predicting that Ohioans’ care will cost 88% more when the Affordable Care Act takes full effect next year. House Speaker John Boehner held up Taylor’s dubious claim as yet another reason to repeal Obamacare.

“The president sold his health care law to Ohioans as a way to bring down costs,” he said. “Instead, many will pay nearly $200 extra every month while also paying higher taxes.”

No one can yet say precisely how Obamacare will affect insurance costs, but mounting evidence suggests it will slash them for many Americans. In New York, Governor Andrew Cuomo announced Wednesday that people buying their own coverage will see prices fall by more than half when the state’s new insurance exchange opens this fall. And in a new report released Thursday, analysts at the U.S. Department of Health and Human Services found that next year’s rates are coming in nearly 20% below projected levels in the 11 states where insurers have posted their offerings.

“The Affordable Care Act is working to increase transparency and competition among health insurance plans and drive premiums down,” HHS Secretary Kathleen Sebelius said of the new finding. She may well be right.

Until now, people lacking employer-sponsored health plans have had few good options. Young, healthy adults have opted out of the system in droves, leaving those with greater medical needs to pay astronomical prices for minimal coverage. The Affordable Care Act expands the risk pool by forcing everyone to participate and subsidizing coverage for those who need help. It also establishes 50 state-wide insurance exchanges where insurers can advertise four levels of coverage (bronze, silver, gold and platinum), and consumers can shop for the best deal on the type of coverage they want.

It’s a market-based solution, not a government takeover, and the early evidence suggests it’s working as intended. “The individual mandate creates a bigger market and the exchanges force insurers to compete for their share of it,” says Timothy Jost, a health policy expert at the Washington and Lee University Law School. “When a high-rate company sees competitors offering the same coverage for less, it tends to adapt quickly.”

In the new federal report, analysts compare the best rates insurers have posted for 2014 with an “expected rate” derived from past projections by the Congressional Budget Office. The expected cost of silver-level coverage was $392 a month, but the actual 11-state average was $321—or 18% less. The best available rate for 2014 came in below the expected level in 10 of the 11 states where insurers have listed their prices (Vermont was the sole exception). Here’s the full breakdown:

Keep in mind that these are just list prices. People earning up to 400% of the federal poverty level—$45,960 for an individual, $94,200 for a family of four—will receive tax credits to help offset the cost. It’s also worth noting that Ohio is not in flames. The full price of a silver-level health policy ($333 a month before tax credits) is 15% below the expected rate. And as the report’s authors note, insurers are still posting rates there. Free-market capitalism—a.k.a Obamacare—may yield Boehner’s constituents a better deal yet.