Andrew Harrer/Bloomberg

The Obama administration is predicting a meager increase next year in the number of Americans with private insurance through the Affordable Care Act — a forecast, far below previous government estimates, that signals the obstacles to attracting people who remain uninsured.

Health and Human Services Secretary Sylvia Mathews Burwell announced Thursday that an expected 10 million Americans will be covered by late 2016 by health plans they bought on the federal and state insurance exchanges created under the law.

That figure is just half the most recent forecast by congressional budget analysts, who have long expected 2016 to usher in the biggest surge in enrollment. The number represents a marginal increase from the 9.1 million Americans the administration believes will have ACA health plans by the end of this year.

The anemic projection comes as the sprawling law is entering a new phase. Having survived the disastrous 2013 rollout of HealthCare.gov, the federal exchange’s online enrollment system, and weathered two Supreme Court challenges, the ACA has moved past critics’ early hopes that the law might quickly collapse.

Proponents note that the statute has been responsible for the biggest gain in insurance coverage in decades. But questions linger over whether it can reach deep into the pockets of the nation’s most intractable uninsured populations and whether people who currently have health plans through the marketplaces will decide that the coverage is worth keeping.

The ACA’s third open-enrollment period starts in barely two weeks.

The new HHS prediction represents the second time that the administration has significantly undercut that of the Congressional Budget Office. The latest discrepancy is much greater than a year ago, when federal health officials predicted that enrollment through the insurance marketplaces would reach up to 9.9 million by the end of 2015, compared with the CBO’s 13 million.

Some health-policy experts suggested that the tepid 2016 forecast may be partly strategic. “The ACA has become such a numbers game,” said Larry Levitt, a senior vice president of the Kaiser Family Foundation. “So, yes — the optics of a low projection are bad, but not nearly as bad as not succeeding when the final enrollment numbers come in.”

Still, substantive forces are at work behind the calculation. According to HHS estimates, about 10.5 million uninsured people are eligible to buy a health plan on the exchange, and they are proving more difficult to reach than those who bought coverage early on.

In addition, federal health officials point out that the dynamics of insurance coverage have not been playing out as analysts expected. Fewer employers have dropped health benefits for their workers, and fewer consumers have switched from older policies they purchased on their own. Both factors, HHS officials say, play into their projection of how many people are likely to gravitate to the exchanges.

HHS contended on Thursday that exchange enrollment, originally pegged to reach 24 million within several years, is not plateauing but is instead on “a much longer path towards equilibrium,” as a senior official said.

Congressional Republicans, who have been trying to tear down the sprawling health-care law from its beginning, immediately sounded skeptical. “For the second straight year, the latest #Obamacare enrollment goal falls below CBO predictions,” House Majority Leader Kevin McCarthy (R-Calif.) tweeted.

If enrollment were to taper off sooner and lower than expected, it would raise questions about whether a cornerstone of the ACA is working. At the same time, the government would save money on subsidies the law provides to most individuals with coverage through the exchanges.

In a telephone briefing for reporters, Burwell called the 2016 goal of 10 million “strong and realistic.” In its most recent estimate, the CBO predicted in June that 20 million Americans would have such coverage next year.

Burwell reiterated that the administration’s outreach efforts during open enrollment will focus on that group of 10.5 million uninsured Americans eligible for the exchanges, who remain a challenge despite the law’s increasing financial penalties for going without coverage. The sign-up period also will test consumers’ willingness to renew insurance that tends to come with greater out-of-pocket expenditures and a smaller choice of doctors, compared with the typical health benefits Americans get through their employers.

Asked how much money HHS will devote to outreach, Lori Lodes, communications director for the department’s Centers for Medicare and Medicaid Services, skirted the question. She said that CMS, which oversees the exchanges, would intensify its marketing in several communities with large uninsured numbers, including parts of Texas, Florida, northern New Jersey and Atlanta.

About half of the targeted group are young adults — a part of the population in which insurance rates historically have been low, HHS officials said. More than a third are members of minority groups. And 4 in 5 have less than $1,000 in savings.

The new enrollment forecast shows that the administration expects to attract one-fourth to one-third of these people by the end of 2016, with 2.8 million to 3.9 million gaining insurance. Officials also predict that up to 1.5 million additional people will switch from other individual policies to exchange plans.

But some of the 9 million-plus people who currently have such coverage will drop it, and some people who pick 2016 insurance policies during open enrollment will not keep them in effect.

That brings the administration’s bottom-line figure to roughly 10 million Americans covered on the exchanges as of December 2016.

“This open enrollment is going to be a challenge,” Burwell said Thursday, “but having fewer uninsured Americans to sign up is a good problem to have.”