Dr. Curtis Whitehair (C) and resident Dr. Christopher Karam (R) watch as Dr. Eric Wisotzsky (L) measures the arm of cancer patient Angela Milhouse, 57, during her checkup at the National Rehabilitation Center on September 21. (Linda Davidson/THE WASHINGTON POST)

The Obama administration cut a major planned benefit from 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 President Obama’s signature legislative achievement.

Republican critics of the law immediately said the decision proved that the legislation is unsound and unsustainable. Every major GOP presidential candidate has pledged to work to repeal it.

Because the insurance program had been projected to reduce the federal deficit by $86 billion over the next 10 years, terminating it complicates the nation’s 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 (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 illness or disability, to be used to pay for even nonmedical needs, such as making a house wheelchair-accessible or hiring a home caregiver to assist with basic tasks.

The program was to be entirely self-financed with the premiums participants paid. Obama officials said that presented them with 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, to the point of the program’s collapse.

For the past 19 months, experts in the administration had searched for ways to get around the conundrum.

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

Rep. Phil Gingrey said the finding was long overdue. The Georgia Republican, 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 Services determined that the program was at significant risk of failure.

“I feel justified and vindicated,” Gingrey said. 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 program was an isolated case whose practicality was questionable from the beginning. Indeed, she said, for this very reason, the law stipulated that the secretary of health and human services had to certify that any CLASS Act plan she designed would be solvent for the next 75 years before she could implement it.

“There is a very clear difference between that kind of uncertainty and the rest of the law,” Glied said.

Meanwhile, consumer advocates accused the administration of giving up too easily.

“I’m very disappointed,” said Connie Garner, who helped draft the CLASS Act while on the staff of the late senator Edward M. Kennedy (D-Mass.).

“CLASS is a critical backstop, giving working families a tool to protect themselves from being one illness or injury away from poverty,” said Garner, who directs a group called Advance CLASS Inc. “The president promised to implement this program. We expect him to keep that promise.”

The program was a long-cherished goal of Kennedy, whose support helped ensure that it was folded into the larger health-care measure despite resistance from prominent Democrats and even the White House.

Its path to inclusion was also eased by projections that, at least initially, it would boost the federal balance sheet by tens of billions of dollars. This was because the law barred the program from paying out benefits for the first five years. So by adding the program to the health-care legislation, Democrats were able to substantially increase the deficit savings they could claim for the law as a whole.

The move helped gain the measure’s passage. But on Friday, Senate Minority Leader Mitch McConnell (R-Ky.) highlighted the strategy’s downside, saying in a statement: “The Obama administration today acknowledged what they refused to admit when they passed their partisan health bill: The CLASS Act was a budget gimmick that might enhance the numbers on a Washington bureaucrat’s spreadsheet but was destined to fail in the real world.”

Staff writer Peter Wallsten contributed to this report.