In a town hall hosted by CNN on Monday (transcript here), Republican Speaker of the House Paul Ryan insisted, "Obamacare is collapsing. It is really -- it is collapsing under its own weight" and "Obamacare is not working," adding that "We've got dozens of counties around America that have zero insurers left."
Update 2017 August 26: I missed the fact Speaker Ryan's office had acknowledged that what Ryan said was incorrect, as pointed out by Politifact in an article rating Ryan's claim false at the "pants on fire" level.
In fact, when Ryan spoke there was one county in Ohio -- one county, not "dozens" -- with no insurer signed up to offer individual policies on the exchanges next year. But that county now has an insurer, so the number of so-called "blank counties is now zero. This despite the fact that the Trump administration has been doing a variety of things to destabilize the healthcare market in order to make his dire predictions come true. (For more on that, see this previous post. See also the Kaiser Family Foundation's report on insurance availability.)
Ryan also claimed that nearly half of counties would have only one insurer. That might or might not be true, but a more important number is how many people will have a choice of health insurance companies, and that turns out to be more than 3/4. (See Kevin Drum's concise post about that.)
It's true that health insurance premiums have increased across the board (not just for individual policies on the Obamacare exchanges) mainly because the costs of healthcare have increased. But because of the way subsidies work, the vast majority of people buying individual policies are sheltered from those increases. The deductibles are another matter. For low-income working families who have silver plans, the Affordable Care Act offers help with paying the deductibles. People who are better off still have to pay them, which isn't good. But prior to the ACA, they might not have been able to get health insurance at all, or the insurance they got might well have been cheap but largely worthless.
For that matter, Republicans have historically favored high-deductible plans to give patients "more skin in the game," so they will supposedly shop around for cheaper doctors and hospitals and medical tests, as if that were a practical option for most people. And of course the "repeal and replace" bill Speaker Ryan favored would have left more than 20 million more Americans uninsured.
Update 2017 September 15: Last week a company suddenly pulled out of next year's individual health insurance market in Virginia, leaving 48 counties without coverage. Today, however, Anthem agreed to fill the gap, which again everyone in the U.S. will be able to find a policy in 2018. If the administration would stop trying to sabotage Obamacare (see this post) the situation might not have arisen in the first place.