Tens of thousands of people who discovered that HealthCare.gov made mistakes as they were signing up for a health plan are confronting a new roadblock: The government cannot yet fix the errors.

Roughly 22,000 Americans have filed appeals with the government to try to get mistakes corrected, according to internal government data obtained by The Washington Post. They contend that the computer system for the new federal online marketplace charged them too much for health insurance, steered them into the wrong insurance program or denied them coverage entirely.

For now, the appeals are sitting, untouched, inside a government computer. And an unknown number of consumers who are trying to get help through less formal means — by calling the health-care marketplace directly — are told that HealthCare.gov’s computer system is not yet allowing federal workers to go into enrollment records and change them, according to individuals inside and outside the government who are familiar with the situation.

“It is definitely frustrating and not fair,” said Addie Wilson, 27, who lives in Fairmont, W.Va., and earns $22,000 a year working with at-risk families. She said that she is paying $100 a month more than she should for her insurance and that her deductible is $4,000 too high.

When Wilson logged on to HealthCare.gov in late December, she needed coverage right away. Her old insurance was ending, and she was to have gallbladder surgery in January. But the Web site would not calculate the federal subsidy to which she knew she was entitled. Terrified to go without coverage, Wilson phoned a federal call center and took the advice she was given: Pay the full price now and appeal later.

Now she is stuck.

“I hope,” she said, “they really work on getting this fixed.”

The Obama administration has not made public the fact that the appeals system for the online marketplace is not working. In recent weeks, legal advocates have been pressing administration officials, pointing out that rules for the online marketplace, created by the 2010 Affordable Care Act, guarantee due-process rights to timely hearings for Americans who think they have been improperly denied insurance or subsidies.

But at the moment, “there is no indication that infrastructure . . . necessary for conducting informal reviews and fair hearings has even been created, let alone become operational,” attorneys at the National Health Law Program said in a late-December letter to leaders of the Centers for Medicare and Medicaid Services (CMS), the agency that oversees HealthCare.gov. The attorneys, who have been trying to exert leverage quietly behind the scenes, did not provide the letter to The Post but confirmed that they had sent it.

A CMS spokesman, Aaron Albright, said, “We are working to fully implement the appeals system.”

Three knowledgeable individuals, speaking on the condition of anonymity about internal discussions, said it is unclear when the appeals process will become available. So far, it is not among the top priorities for completing parts of the federal insurance exchange’s computer system that still do not work. Those include an electronic payment system for insurers, the computerized exchange of enrollment information with state Medicaid programs, and the ability to adjust people’s coverage to accommodate new babies and other major changes in life circumstance.

The exchange is supposed to allow consumers who want to file appeals to do so by computer, phone or mail. But only mail is available. The roughly 22,000 people who have appealed to date have filled out a seven-page form and mailed it to a federal contractor’s office in Kentucky, where the forms are scanned and then transferred to a computer system at CMS. For now, that is where the process stops. The part of the computer system that would allow agency workers to read and handle appeals has not been built, according to individuals familiar with the situation.

In the meantime, CMS is telling consumers with complaints about mistakes to return to the Web site and start over. “We are inviting those consumers back to HealthCare.gov, where they can reset and successfully finish their applications without needing to complete the appeals process,” said Albright, the agency spokesman. The rationale is that, since the computer system is working better now, it’s less likely to make mistakes.

Agency officials have no way of knowing how many people have taken that advice, according to two individuals familiar with the situation. The computer system containing the scanned appeals forms cannot yet communicate with HealthCare.gov’s enrollment database, so it is impossible to cross-check the information.

Across the country, a few specialists trained to help people enroll in the health plans point to examples in which withdrawing an application and starting over has solved the problem. But that is not a solution for everyone.

Starting over would not help Addie Wilson, for example, because she has already begun to pay for her new insurance and would have no way to get her money back. A few days before Christmas, Wilson was hospitalized with what turned out to be a gallbladder so infected that doctors inserted a drain so it would be safer by the time they operated — the first surgery of her life. She needed a health plan because her employer, the organization Home Base, was cutting off the Blue Cross-Blue Shield coverage she and her co-workers had, reasoning that they could find better choices on the new marketplace.

Given her salary, Wilson knew she was eligible for federal subsidies to help pay for her coverage. She was discharged from the hospital on Dec. 23, the insurance sign-up deadline; she did not yet know that CMS had quietly reset its computers to give people one more day to enroll. It had been weeks since the Obama administration had announced that the system was working smoothly, so she could not understand why the HealthCare.gov screen on her laptop, which should have calculated her subsidy, stubbornly refused to appear. She asked her boyfriend to try on his computer and her father to try on his. Nothing worked.

She called HealthCare.gov’s toll-free number, where, she said, a woman on the other end tried typing and then told her, “Well, it’s not working for me either.” The woman recommended that she choose a health plan at the too-high price and file an appeal. Since her Blue Cross coverage would end Dec. 31, she went back onto HealthCare.gov and picked a plan.

A failure to compute a subsidy is among a variety of mistakes the computer system has made. Another involves what some CMS and state Medicaid officials refer to as “loopers.” These are people who applied for coverage on HealthCare.gov and were told that their income was low enough to qualify for Medicaid. But when they went to their state Medicaid agency, they were told they were not eligible after all, and should get a private health plan through the marketplace. So they have “looped” back to the federal system, which is unable to fix the mistake.

The letter from the National Health Law Program describes families who are appealing for other reasons. In one instance, a North Carolina couple were told that they were eligible for subsidies to buy private policies and that their son was eligible for the Children’s Health Insurance Program, which is public insurance for children of working-class families. But the computer told them that their daughter was eligible for nothing — an obvious mistake. At the time of the letter, the family was uninsured while waiting for a decision on its appeal.

In Fairmont, Wilson is waiting, too. In early January, she contacted her new health plan about her missing subsidy and asked what to do. She was told to pay the full insurance premium — $215 a month. She did. The next day, Brandon Williams, an enrollment counselor at a local health clinic, helped her check HealthCare.gov again. This time, the computer worked properly and showed that, with the subsidy, her monthly premium should be just $106 and her yearly deductible $617, not $4,750.

Wilson and Williams called the online marketplace and, after three hours on the phone, got only a promise from a supervisor that Wilson would hear from CMS’s “advance resolution team” within five days. The call didn’t come.

Wilson’s scheduled outpatient surgery turned into an expensive, five-day hospital stay after her doctors discovered her gallbladder had gangrene. Home after the ordeal, and dreading the hospital bill and her big deductible, Wilson called Williams, and they tried to reach the advance resolution team. They couldn’t get through. When the call from the team finally came, she said, a knowledgeable-sounding man told her, “The system is not set up to go into someone’s account and correct a mistake.”

With Williams’s help, she has filed an appeal. And she is waiting — waiting to be healed enough to drive so she can go back to work, waiting for someone to decide that she deserves her money back.

“These little kinks should have been worked out prior to this thing being launched,” she said. “This is one more thing stressing me out.”