NEW YORK — Included among the many uplifting economic numbers released by the Census Bureau on Tuesday was a remarkable one about health insurance: Only 9.1 percent of Americans do not have coverage, the lowest level ever recorded by the agency.

That figure is down from 13.3 percent in 2013, before the major provisions of the health care law signed by President Obama went into effect.

Another government study, released last week, looked at the first part of 2016 and found that the uninsured rate had fallen even further, to 8.6 percent.

So does that mean the Affordable Care Act is solving the puzzle of getting people covered, a major goal of the law?

It certainly looks that way. About 18 million more people have coverage now than in 2013.

But the new numbers also highlight where the law is not working well — and how difficult it will be to drop the uninsured rate much lower.

Many states have continued to resist the Obama administration’s entreaties to expand their Medicaid coverage, leaving millions of poor Americans with no affordable health insurance options. And the marketplaces created under the law, in which middle-income people without insurance can buy policies, are struggling in states across the country.

Some insurers are dropping out, and others are sharply raising prices. In New York City, for example, rates for a benchmark plan could go up an average of 16 percent, according to one analysis.

If the marketplaces do not stabilize, the drop in the uninsured rate could stall or even reverse.

Adding to the uncertainty is the hazy future of the health care law. Donald Trump and Republicans in Congress have vowed to repeal it if they get the chance. And even if the Democrats are in control, there is an array of competing proposals on how to adjust the law.

“The way I would frame it is, this isn’t just about whether the Affordable Care Act works,’’ said Dr. Benjamin D. Sommers, an assistant professor at Harvard’s School of Public Health and former researcher for the Health and Human Services Department, who has analyzed the remaining uninsured population. “It’s also about whether the effort to expand coverage has gone far enough.’’

The Affordable Care Act was not intended to cover everyone, the way single-payer systems in many other countries do. Undocumented immigrants, for example, are largely shut out of the health insurance system. And because the system requires people to actively sign up for insurance and often pay a premium, there will always be some Americans too independent — or isolated — to seek insurance.

But the law was certainly written to get insurance to far more people.

The Medicaid expansion, for example, is meant to expand coverage to all Americans earning below a set income threshold — about $16,000 for a single person. Adoption of the program has been substantial. But the Supreme Court dealt a major blow to that plan in 2012. The court determined that states could decide whether to expand, and 19 have still declined to do so.

Those decisions leave more than 3 million people who are in poverty uninsured and without good options for obtaining health insurance. The law was written to give poor people coverage through Medicaid, not the private marketplace, so it does not provide financial assistance for buying coverage. The census report highlighted an increasing gap in the uninsured rates between states that expanded their programs and states that did not.

There is another large group of low-income Americans — about 9 million, according to recent calculations from the Urban Institute — who are eligible for Medicaid or the related Children’s Health Insurance Program but have not signed up.

The online marketplaces, which play a critical role under the law in reducing the number of people without coverage, also remain volatile. Fewer people than expected have signed up for plans through the marketplaces, and the enticements are not improving. Prices are set to rise substantially next year. And in many places, people who enroll will have fewer insurers to choose from. Millions of people qualify for subsidies to buy into the plans. But many middle-class people who qualify for small subsidies have still found the plans to be unaffordable.