Few government agencies touch the lives of more Americans than the Social Security Administration — the agency pays $1.4 trillion in benefits to more than 71 million people every year.

But Social Security has been grappling with a customer service mess that threatens to grow worse before it gets better. The problems include long wait times on the agency’s toll-free phone line, a large backlog in disability applications and a growing problem with overpayments to low-income beneficiaries.

Many of the problems stem from austere administrative budgets imposed by Congress over the past decade. Since 2011, congressional cuts to the agency’s customer service budget total 17 percent after adjustments for inflation, and staffing fell to a 25-year low last year, according to an analysis by the Center on Budget and Policy Priorities, a progressive research and policy organization. At the same time, the number of beneficiaries rose by 22 percent over the past decade.

The current budget battle in Congress could worsen the situation. The Biden administration has requested a $1.3 billion increase in the S.S.A.’s customer service budget for next year, while House Republicans have proposed a $250 million cut in that spending. Decisions about federal spending have been pushed into early 2024 under an agreement reached last month.

Even a decision to keep funding steady next year would translate into slower service as the S.S.A. uses more of its resources to meet rising fixed costs, such as scheduled pay increases, employee benefits and office rents. The agency’s fixed costs rise $600 million to $700 million annually.

“The budget situation is bad now, and it’s safe to say it will get worse next year,” said Kathleen Romig, C.B.P.P.’s director of Social Security and disability policy. “The problems get progressively worse over time and compound.”

The funding problems come while the S.S.A.’s leadership is in transition. President Biden has nominated Martin O’Malley, a former governor of Maryland and a former presidential candidate, as the agency’s permanent director, and Mr. O’Malley is awaiting Senate confirmation. He would replace Kilolo Kijakazi, who has served as acting director since July 2021, when the president fired Commissioner Andrew Saul, an appointee of President Donald J. Trump.

Dr. Kijakazi is a public policy expert who has written extensively on Social Security, income, wealth and race. In an interview, she pointed to several areas of progress during her tenure, including re-establishing walk-in traffic at the agency’s 1,230 field offices after a pandemic shutdown, using this year’s $707 million increase in customer service funding to add 7,900 employees.

But Dr. Kijakazi said that the administrative budget problems remained a central issue.

“It will take years of sustained, sufficient funding and collaboration both within the agency and with outside partners for the agency to recover from a work force and service crisis that was years in the making,” she said.

Training new workers typically takes more than a year because Social Security rules are so complex. And the current short-term extension of spending forced the agency to freeze hiring.

“If the final budget for S.S.A. maintains level funding, the hiring freeze will continue throughout the year,” she added. “Given expected attrition over the course of the year, we will not be able to replace the people who leave.”

Further funding cuts were proposed earlier this year by Republicans as part of a broader budget plan they said was aimed at “reining in wasteful bureaucracy and enhancing oversight and accountability.” But Dr. Kijakazi said the cuts would force more painful choices, including furloughs and limited service hours, field office closings and halting of a badly needed modernization of the agency’s information technology.

All of that would come as the agency is already confronting major challenges.

The waiting time on S.S.A.’s phone line, which is crucial for people with questions about benefits or those applying for benefits, averages 36 minutes. Average wait times have fluctuated over the past decade, but in 2013 the average wait time was 10 minutes. The agency recently began using a modernized toll-free phone system, but noted that more trained employees will be needed to reduce wait times.

There is a backlog of more than one million people waiting an average of seven months for initial decisions on disability benefit applications — a process that has been slowed by staffing issues at the agency and in state governments, which receive S.S.A. funding to determine applicants’ eligibility at the local level.

The agency also is under fire over overpayments of benefits that have led the agency to claw back billions of dollars, with some people receiving notices that they owe tens of thousands to the S.S.A. Repayment is due in 30 days, although the notices explain that beneficiaries can file appeals or request waivers if they believe the overpayment was not their fault and they cannot afford to pay it back. The overpayment problem has affected some of the most vulnerable beneficiaries: recipients of disability benefits and Supplemental Security Income, the program that supports very low-income Americans.

A key cause of the problem is adjustments to benefits required under the law when a beneficiary’s income, work status or amount of assets change. The S.S.A. is developing a system to tap third-party payroll data that will reduce reporting responsibilities of beneficiaries and improve efficiency. But progress has been slow — the project was authorized by Congress in 2015, and a proposed rule for starting the system won’t be filed until next month, the S.S.A. said Friday.

But a new report from the agency points to overpayment problems in the retirement and disability programs. The S.S.A. notes that in these programs, only one half of 1 percent of paid amounts were overpayments, and that the study finding is based on a sample that may not represent a long-term trend.

Dr. Kijakazi notes that a review is underway to determine whether other procedural changes could address the broader overpayments problem. But she said that the error rate on overpayments was small in the context of a huge program like Social Security and argued that the problem stemmed mainly from changes in people’s income or work status that had not been reported.

“We are required by law to recapture overpayments,” she said. “We understand how upsetting this likely is for anyone receiving a letter.” She added: “If members of Congress and the public do not want us to proceed in the way that we are with respect to overpayments, they only need to change the legislation.”

The law, however, does give the S.S.A. authority to waive recovery of overpayments under certain circumstances, Ms. Romig said. “There’s a lot they could be doing to make overpayments less harmful to people, and they’re not doing it,” she said.

The overpayment problem also underscores the challenges facing an agency working with outdated information technology — and a work force under strain.

Earlier this year, the Social Security Administration placed last in a ranking of the best places to work in the federal government — down sharply from just a decade ago, when it was consistently ranked as one of the best.

“Things are not getting any better,” said ​​Jessica LaPointe, president of the American Federation of Government Employees Council 220, which represents employees at Social Security field offices and call centers.

Ms. LaPointe said she hoped that the appointment of a permanent commissioner would help. “We think he really will do what he can with the limitations of our budget, but we need Congress to actually fund S.S.A.’s operating costs,” she said, referring to Mr. O’Malley.

“We’re so crippled and demoralized by these proposed budget cuts,” Ms. LaPointe said. “When the public is sitting and waiting for needed services, it creates a very frustrating situation for the customer and for employees who feel like we’re failing in the mission we have.”