WASHINGTON – Marc Schenker, a U.S. Air Force veteran in Fort Lauderdale, Fla., is having surgery this month to remove a golf-ball-size hernia – but not at a veterans hospital. Schenker, 67, said he had given up on the Veterans Affairs hospital in Miami after waiting months to get the procedure scheduled and had turned to a private surgeon instead, using Medicare.

“It’s frustrating and infuriating that there are so many dedicated doctors who work for the VA but it seems impossible to get to them,” said Schenker, who served with the Tactical Air Command during Vietnam. “They’re serving too many people.”

In interviews and in hundreds of responses to a questionnaire posted by the New York Times, veterans around the country expressed frustration with delayed access to care and what many described as an impenetrable and unresponsive bureaucracy at department hospitals and clinics, even as many praised the quality of care they received once they saw doctors.

Their complaints – including repeated canceled appointments and unreturned calls, lengthy waits for appointments and rapid turnover in physicians – give voice to findings by the inspector general of the Department of Veterans Affairs last week that officials at the veterans medical center in Phoenix and elsewhere used a variety of schemes to hide increasingly long waits for medical care.

A department audit released Friday confirmed the systemic nature of the abuse, finding that in nearly two-thirds of facilities there had been at least one instance of reporting false wait-time data. The secretary of Veterans Affairs, Eric Shinseki, who had come under bipartisan attack for the widening scandal, resigned on Friday after presenting the audit to President Obama.

Many veterans interviewed Friday said they did not fault Shinseki for the problems that have plagued the department, which is straining to accommodate a rising tide of veterans from not just Iraq and Afghanistan, but also Vietnam and earlier wars. Yet some expressed relief that their grievances had finally been confirmed, and said they saw Shinseki’s departure as an opportunity for an aggressive overhaul of the veterans’ health-care system, the nation’s largest, with 150 hospitals and 820 outpatient clinics serving more than 8 million veterans.

“I think that firings need to go on all over the country,” said Claude V. D’Unger, 68, an Army veteran in Corpus Christi, Texas, who said he had all but stopped seeking care at the department after he could not get a timely CT scan to check a nodule on his lung. After calling for an appointment and being told that he would have to wait at least two months, D’Unger said, he contacted a private doctor who performed the scan the next day.

The Phoenix medical center is at the center of the scandal, with a department investigation confirming last week that 1,700 patients were not placed on the official waiting list for doctors’ appointments and may never have received care. Veterans outside the hospital Friday had differing views on whether Shinseki’s resignation would change anything.

Ralph Munoz, 63, an Air Force veteran who spent half a year in Vietnam, said waits for appointments had grown longer since he started receiving care at the Phoenix center in 1998. His biggest concern now is that his prostate cancer, which had been in remission, was detected again May 9, but his next medical appointment is not until Aug. 18.

“There are other guys ahead of me,” he said, adding that he hoped the department would outsource more care to private doctors, as it has promised to do.

But Kimberly Mitchell, 53, who served in the Navy from 1979 to 1983, said she had been consistently happy with the care she had received at veterans hospitals, including surgery for a noncancerous brain tumor in Denver in 2010. Her comments echoed many responses to the New York Times questionnaire that described care in the system as superb and in some cases said it did not require long waits.

“I thank God every day for the VA,” Mitchell said.

Some veterans, like Bill Gay of Bethany Beach, Del.,said they saw the crisis as an opening for the privatization of pieces of the department’s health-care system. Gay, 69, a former Marine who was badly wounded during the 1968 siege of Khe Sanh, said the department should pay for veterans in rural areas to see private doctors instead of requiring many to travel long distances to the nearest veterans hospital or clinic.

Whoever replaces Shinseki “ought to be a junkyard dog,” Gay said, adding, “The opportunity is here to make radical change.”

In the meantime, veterans dealing with crowded, bureaucratic medical centers need to be aggressive self-advocates, said Max Gruzen, 74, of San Diego.

Many veterans said they were shocked at the high turnover of doctors.

Dr. Stephen Halvorson, a physician at a Veterans Affairs clinic in Bozeman, Mont.,said he was leaving the job after two years because of a litany of frustrations, mostly with administrative burdens.

“It’s about utter aggravation,” Halvorson wrote in an email, “and the realization that despite your professionalism, your training, your intelligence, it’s unlikely that you’ll be able to make a meaningful contribution.”

In an interview, he said he had felt stifled by administrators “trying to create rules and standards and metrics” that might have hurt patient care.

“It’s a joke – what’s this week’s, this month’s, this quarter’s new metric that we are all anguishing about?” Halvorson said. “I would love to instead see primary care docs asked what they need: ‘How can we help you guys out?’ ”