The Veterans Administration operates 80,000 hospital beds, pays for the care of 40,000 nursing home patients, handles 16 million outpatient visits a year and employs 194,000 medical workers; it has more employes than any other civilian agency in the government.

And yet it may not be big enough.

The reason is that Congress has directed the VA to provide free health care to all veterans over 65 if space is available, creating one of the fastest-growing benefit programs in the government.

The number of veterans over 65 will more than double to 9 million in the next 15 years, forming a demographic tidal wave that threatens to swamp the system and nearly triple the VA's medical budget to $25 billion.

Until now, Congress has been unwilling to say no to the nation's 26 million veterans, one of the most sophisticated and aggressive lobbying groups in the country.

Now President Reagan is trying to put the brakes on this program that has grown like topsy outside the rest of the health care system. Among other things, he wants to end free health care for veterans over 65 who earn more than $15,000 a year, except those with service-connected disabilities.

Critics say there are several reasons for the VA's dilemma:

* Sixty-five percent of the patients receiving free care in the VA's 172 hospitals have "non-service-connected" disabilities, normal illnesses that have nothing to do with past military service. The number of service-connected patients treated by the VA has dropped steadily over the last 15 years.

Nearly everyone agrees that veterans injured in service should get free care. But critics question why the VA continues to build costly 1,000-bed hospitals that are several times the size needed to treat those patients.

* There is also debate over the definition of a "service-connected" ailment. If an active serviceman develops one of 40 diseases, from diabetes to peptic ulcers to cirrhosis of the liver, the VA automatically presumes that it is related to his military service. Nor does a serviceman have to be injured on the job to qualify.

"If you're doing a paper work job at Fort Dix, N.J., and get in a skiing accident, you get free health care for the rest of your life, whereas the guy who scaled the walls of Normandy may not be eligible," a Senate aide said.

* The Office of Management and Budget says the VA's figures show that 17 percent of VA patients could be excluded by a $15,000 income limit and that this would save $500 million over the next three years. OMB officials also argue that the VA system is inefficient, noting that the length of stay for some VA patients is nearly double that in private hospitals.

* Some VA hospitals are built in areas where there is a surplus of private hospital beds. This is mainly a product of congressional politics, which has produced bigger and better hospitals for many lawmakers' districts.

The VA says it is turning away more than 20,000 patients a month, but this is difficult to document. A third or more of the VA's hospital beds are empty in such places as Cleveland; Madison, Wis., and Wilmington, Del. And while occupancy is 100 percent at the Charleston, W.Va., hospital, officials there say they turn no one away, although care sometimes is delayed.

VA officials say much of the criticism is unfounded. They say a system that treated only service-connected patients would be too small to be viable, and that turning away more veterans simply would shift costs to the Medicare program.

It is Congress, these officials say, that has mandated free care for up to 80 percent of their patients by continually expanding the list of beneficiaries. That list now includes veterans of World War I and the Spanish-American War, veterans exposed to atomic tests, veterans who handled the defoliant Agent Orange, former prisoners of war and Vietnam veterans with adjustment problems.

VA officials also say that it is unfair to compare their hospitals with private facilities because many of their patients suffer from alcoholism and other complications or have no families to care for them.

Veterans' organizations are particularly riled about Reagan's proposed means test, saying it would force many veterans over 65 to turn to Medicare, which they contend is more expensive than the VA system.

"I don't think it would save the government a penny," said R. Jack Powell, executive director of Paralyzed Veterans of America. "If we merely send them to a more expensive system subsidized by the federal government, what have we gained?"

Cooper T. Holt, Washington director of the Veterans of Foreign Wars, said the administration's aim "is to dismantle the VA system, and we don't like that . . . . We're not going to let someone tear it apart."

But VA Administrator Harry N. Walters insists that there is no hidden agenda. "If anyone is going to try to shrink the VA system in the face of burgeoning demand, I wish them a steel armor plate so they don't get mutilated in the combat," he said.

At the heart of this debate is the question of who the VA system is supposed to serve.

An income limit, said Philip Riggin of the American Legion, "approaches the government reneging on an obligation that we felt had been made to us. The veteran has expected certain things from the government, and one of them is health care."

Sen. Alan K. Simpson (R-Wyo.), former chairman of the Senate Veterans Affairs Committee, disagrees. "I'm a veteran," he said, "and I don't remember this unwritten contract, when I went off to Germany, that I was entitled to this and that on down through the decades."

The public's image of the veteran, Simpson said, "is a guy going over a trench with a tin hat on. They forget that maybe only 2 million of the 30 million veterans were ever involved in combat. Millions never left the United States. Some didn't even serve a year."

The budget numbers reflect the high stakes. Since 1970, health-care outlays for veterans have increased fivefold, to $9 billion. In the next 15 years, the VA says, it will need a 68 percent increase in hospital beds; its nursing home patients will more than double to 97,000, and the number of patients receiving home health care and other alternate treatments will jump from 15,000 to 760,000.

Few officials contend that the VA can afford to treat all these veterans. Walters warned Congress last month about creating "false expectations for our older veterans."

Reagan's solution is a means test to be set at $15,000 for a veteran with one dependent. A veteran's assets, except for a home and a car, also would be considered, and those over the limit would be turned away by the VA until they spent a substantial amount on medical care.

Congress abolished an earlier VA means test in 1970 on grounds that it was excluding few patients. Now all veterans over 65 are eligible if space is available, while those under 65 are required only to sign a "poverty oath" saying they cannot afford to pay for their care.

Many lawmakers have been cool to the means test idea. "Most of our patients are not affluent," said Rep. G.V. (Sonny) Montgomery (D-Miss.), chairman of the House Veterans Affairs Committee. "There might be a few who abuse it, but it's not many." If some veterans are denied admission to VA hospitals, he said, "they would die earlier; they would die in pain."

"In our urban centers, the VA hospitals have become the indigent ward," said Rep. Robert W. Edgar (D-Pa.). Besides, he added, "What does $15,000 mean if you've got two kids in college and a wife who's infirm?"

Former VA medical director Donald Custis, a consultant to the Paralyzed Veterans of America, said the means test would be costly and cumbersome to administer and is simply a budget-cutting gimmick. "For every veteran found to be taking the poverty oath in vain, there are a dozen standing in line to take his place," he said.

"There are VA hospitals that could be closed," Custis added. "Some of them are remote and obsolete." But he said congressional politics makes it impossible to close inefficient hospitals.

Simpson agreed, saying, "The way a congressman receives awards from veterans' groups is to plant as many veterans' facilities as he can in his district. It's really something to watch."

Yet, Walters said, "All you have to do is threaten to close a VA hospital in Dayton, and you'll find out the importance to the community of having that hospital there . . . . Some people say that's pork barrel. But it's a grass-roots feeling."

The VA has been building such mammoth facilities as a $252 million, 1,047-bed medical center in Houston. But no project can be approved without strong congressional backing.

The VA, for example, agreed to a $128 million renovation of a VA nursing home and clinic in Philadelphia after Edgar, one of the city's representatives, became chairman of the House subcommittee on VA health care. The 1950s facility needed replacement but had failed to make the VA's list for five years. An equally old VA hospital in Baltimore continues to be denied funding; Maryland has no one on the two veterans committees.

Edgar conceded that Congress has approved hospitals in poor locations, but said the administration "wants to deal with the aging veteran problem by restricting service."

The VA must find innovative ways to deliver care, Edgar said. "We've piled onto the VA all these extra programs," he said. "We took $25 million and set up geriatric research centers. The VA didn't want them; now the hospitals are begging for them."

There are nearly 10,000 VA nursing home beds today compared with 250 in 1965. Demand for private nursing care paid for by the VA is so great that members of Congress routinely intervene to keep patients in these facilities.

"It doesn't look like we'll be able to build enough nursing homes to do what's required for veterans," Walters said. "We couldn't do it physically."

The fate of Reagan's plan may depend on the influence of veterans' groups. If the proposal is in danger of passing, the VFW's Holt said, "We could generate a million letters in six weeks."

Simpson said he is accustomed to being "stoned" by veterans protesting benefit cuts. "The guys who fought the great fight, who left chunks of their bodies on foreign soil, they're not the ones who raise hell," Simpson said. "The ones who raise hell sat it out.

"You've got 30 million veterans and their wives, widows and orphans. You're dealing with potentially half the citizens in the country. That's how that budget got to be $26 billion."