But the ACA has proven to be surprisingly resilient. Attempts to weaken the market through cutting back programs to sign up new enrollees, creating work requirements for Medicaid recipients, and promoting alternative insurance models have moved forward through various executive orders and rule changes by federal agencies. Yet none of those efforts have had much effect on the ACA markets overall.

The repeal of the individual mandate, which was included in a 2017 tax reform bill, was the most serious challenge to Obamacare so far. The ACA's individual mandate required any American who did not purchase coverage to pay a tax penalty—a measure that was aimed at providing more incentive for people to purchase coverage and therefore create larger, more financially stable insurance pools.

There was widespread concern when the mandate was repealed that the result would be a wave of younger and healthier Americans exiting the ACA markets. This would leave sicker, more expensive patients in the market and result in increasingly higher premiums, which would not be sustainable.

It turns out people like having insurance

The death spiral has not happened so far, according to the KFF report. According to the report, at the end of 2018, ACA insurance premiums had risen about 5 percent as a result of the individual mandate's repeal.

But the report found that premiums were largely steady in 2019, in part because insurers priced plans too high in 2018. "Despite concerns about the continuing impact of the loss of the mandate penalty, the individual market has remained fairly stable through 2019. Enrollment among those not eligible for subsidies declined by 10 percent in early 2019, but individual market enrollment overall appears to be stabilizing, with total market enrollment falling by just 5 percent," the report said.

However, the ACA marketplace is not indestructible, and there are still areas of concern. The KFF report noted that rural areas of the country are "fragile," with fewer carrier options and higher premiums than urban areas. And an analysis by Vox noted that while ACA enrollees who qualify for subsidies are shielded from premium increases, those with higher incomes are struggling to afford rising premium costs.

"The subsidized customers are partly or fully protected from premium hikes, so they kept signing up," the Vox analysis said. "It was the unsubsidized customers, people making 400 percent of the federal poverty level or more, who faced the full brunt of those increases." This resulted in some enrollees leaving the marketplace, but overall the KFF study found the ACA market to be stable.

"Some insurers exited the market in previous years, but others have been successful and expanded their footprints, as would be expected in a competitive marketplace" the report concluded. "Marketplace premiums are decreasing by 2 percent to 3 percent on average in 2020, further indicating that insurers expect the individual market to remain stable. Marketplace enrollment for 2020 is generally steady."

Next up for attempts to end the ACA: a lawsuit that says the law is unconstitutional, since the individual mandate no longer provides a tax framework as part of the law. That complicated proposition is working its way through the courts and is likely to end up in the Supreme Court.

Read more: 

• IRS cuts ACA individual mandate penalty out of tax forms
• 5 possible effects of the ACA ruling, for agents
• 6 ways states are preparing if the ACA is invalidated