Among major issues of the day, perhaps none so stirs the emotions as the current state of health--or lack of it-- of the Social Security system, crown jewel of the New Deal era, which provides retirement and other benefits to 36 million people.

Two out of every three elderly persons get half of their cash from Social Security. All together, the system will pay out $188.5 billion in calendar 1982 in old-age benefits, disability insurance and hospital insurance.

Resisting the now-common conclusion that the system either has to find ways of taking more money in or paying less money out -- or go broke -- the National Council of Senior Citizens argues that Social Security "is sound and durable" and faces only a short- term cash flow problem, mostly due to the recession.

On the other hand, a recent sober study by the New York Federal Reserve Bank concludes that the system is "fundamentally flawed" and needs major changes for both the short and long term:

"The basic problem is that as the program is currently structured, average retirees both now and in the future can expect to receive benefits that, by any measure, are far in excess of lifetime contributions -- the payroll taxes they pay during their working years."

An example cited by the New York Fed: a 65-year-old retiree this year (with a nonworking spouse) will on the average recover his lifetime contributions within nine months after retiring. This retiree or his wife would, according to the life-expectancy tables, continue to receive benefits for 25 years, or until the year 2007.

The New York Fed says that, in effect, the present value of a retiree's benefits is worth many times what he put in. "The difficulties of Social Security," the Fed goes on to say, "are almost entirely the result of the fact that a self-financed system cannot continue to pay out subsidies forever."

Peter G. Peterson, chairman of Lehman Brothers Kuhn Loeb, estimates that the average retiree, who put $7,209 into the system over his entire work career, could receive (he and his spouse together) as much as $520,000 in a "worst case" scenario, in which inflation rates are high and longevity continues to grow.

Defenders of the system suggest that critics are looking at Social Security as if it were a private insurance system, which it is not. The Senior Citizens council admit that the basic trust fund --the Old Age and Survivors Insurance Fund--faces a shortage during the next few years ranging from $61 billion to $231 billion, depending on economic assumptions. They believe that this shortage can be financed, without cutting benefits, by a combination of measures, including advancing the date of payroll-tax increases already scheduled through 1990.

But the short-term problem is real enough for the president to have appointed a 15-member, blue-ribbon, bipartisan commission under economist Alan Greenspan to make recommendations on what to do. They will report on Dec. 31.

In a telephone conversation, Greenspan said that the commission "has already moved the dialogue substantially forward" by getting agreement on the dimensions of the problem -- the need to increase the pot or lower the benefits by $150 billion to $200 billion over the next seven years.

For the Democrats on the commission to have agreed to these aggregates is an important development because, historically, they have contended that minor patchwork could handle most of the problem. Nonetheless, a big political argument remains to be resolved on the question of cutting benefits over the next few years.

As the commission has already concluded, there are only four basic ways of keeping the system intact: advancing the scheduled payroll-tax increases, tapping general revenues, shaving back future cost-of-living adjustments (to perhaps 60 percent, instead of 100 percent), and requiring federal employees to start paying into the system.

But there would still be the longer- term question raised by the New York Fed and the Congressional Budget Office. It is, in short, this: as the postwar baby- boom generation leaves the work force in the years 2010 to 2015 and graduates onto the Social Security rolls, will the remaining labor force be large enough to finance the benefits -- unless a very large foreign immigration takes place?

The New York Fed answers with an unequivocal "No!" By the year 2035, there will be only 1.5 to 2 workers contributing taxes for each Social Security retiree. Back in 1960, there were 5 workers per retiree. By 1980, the ratio had dwindled to 3.3 to 1. But the year 2035 is so far away that politicians in the year 1982, who have to summon up rare courage to deal with the problems of the next seven years, aren't likely to tackle it.