WASHINGTON — The Obama administration ended a major benefit in the 2010 health-care law on Friday, announcing that a program to offer Americans insurance for long-term care was simply unworkable.

Although the program had been dogged from the start by doubts about its feasibility, its elimination marks the first time the administration has backed away from a key piece of what remains of President Obama’s signature legislative achievement.

Republican critics of the law immediately said the decision proved that the legislation is unsound and unsustainable.

Because the program had been projected to reduce the federal deficit by $86 billion over the next 10 years, terminating it complicates the budget picture. It is now estimated that the health-care law will cut the deficit by $124 billion from 2012 to 2021, according to the Congressional Budget Office.

Known as the Community Living Assistance Services, or  CLASS, Act, the program was intended to be purely voluntary and open to all working Americans. It would have provided a basic lifetime benefit of a least $50 a day in the event of disability, to be used for coverage of even nonmedical needs such as making a home wheelchair-accessible or paying a caregiver.

The program was to be entirely self-financed by the premiums participants paid. Obama officials said this presented a problem: If they designed a benefits package generous enough to meet the law’s requirements, they would have had to set premiums so high that few healthy people would enroll. And without a large share of healthy people in the pool, the CLASS plan would have become even more expensive, forcing the government to raise premiums even higher.

For the past 19 months, experts have searched for ways to get around this conundrum.

Kathy Greenlee, assistant secretary for aging at the Department of Health and Human Services, announced their sobering conclusion Friday: “At this point, we do not have a viable path forward to implement the CLASS Act.”

Rep. Phil Gingrey, R-Ga., who sponsored a bill to repeal the legislation, observed that more than a year ago the chief actuary for the Centers for Medicare and Medicaid determined that the program was at significant risk of failure.

Like other Republicans, he predicted that this would be the first thread in the health-care law to unravel. “The bottom line is as people start to understand this bill, you are going to see more and more of a domino effect,” he said.

Sherry Glied, assistant secretary for planning and evaluation at HHS, countered that the CLASS Act was an isolated case whose practicality was questionable from the beginning. “There is a very clear difference between that kind of uncertainty and the rest of the law,” she said.