In our more rhapsodic moments, we like to picture our older citizens getting by nicely, with a tidy savings nest egg, interest drawn at high T-Bill rates and a useful pension provided by a grateful employer, all supplemented by a bit of Social Security.

That's what we like to picture, but it isn't the reality for the majority of the nation's 26 million senior citizens.

The reality is that Social Security is overwhelmingly the basic source of income for the nation's elderly, with private pensions and savings falling far behind and perhaps in poor position to catch up.

Early this year, the President's Commission on Pension Policy reported that in 1950 Social Security accounted for only 28 percent of all retirement, survivor and disability payments in the nation.

But by 1980, it said, Social Security had doubled its share and, in combination with a few other federal programs like railroad retirement and federal employe retirement, accounted for 78 percent of such benefits. Meanwhile, the share of private pension plans decreased to only 14 percent and state and local government plans to only 8 percent.

Whereas all but a handful of aged persons get Social Security, the commission said that in 1978 only 28 percent of the elderly population, or about 8 million people, received any employe pensions. Most who received such pensions were in the middle- and higher-income strata.

According to Social Security Administration studies, about three-fifths of the aged got at least half their income from Social Security in 1976; a quarter got 90 percent.

Figures in the commission report graphically illustrate the role of Social Security: for retirees with incomes of $4,000, Social Security provided 75 percent of income in 1978; for those with incomes of $6,000 it provided 63 percent of income; for those with incomes of $8,500 it provided over half of income, and for those with incomes of $12,000 it was still the largest single source of income at 36 percent. Only for the small number with incomes over $20,000, who got substantial earnings from employment, did it fall to second place.

Social Security thus predominates as a source of income for the elderly and there are reasons to believe that its role may not diminish.

One is that employe pension coverage is no longer growing much, according to the commission. About half the nation's private employes and most of the nation's federal, state and local government workers are covered by pension plans. But the private plans are generally in larger, more well-to-do firms. The uncovered half work mainly in smaller, poorer places that are going to be much less likely to add private pension systems. The rate of new coverage has slowed to a crawl.

There is another problem: inflation, which makes it hard for employers to keep benefits up to speed. Almost no private pension systems are indexed to the cost of living, though many make periodic increases. This means that the value of the benefits has shrunk substantially in this high-inflation era and, in effect, cannot be depended upon. Social Security and related benefits like railroad retirement, however, are by law increased annually to cover 100 percent of the increases in the cost of living as measured by the Consumer Price Index.

Vesting is a third problem for employe pensions. Social Security, which covers virtually every job, simply accumulates credits wherever one works, except in a relatively small number of government jobs. Employer pension systems do not normally provide "portable" credits except in multi-employer plans such as are common in the construction industry, and even there portability is limited to jobs within a single trade.

The absence of portability in employer pension systems makes it theoretically possible for an employe to work in four different jobs during his career, each for just under 10 years, and never vest in pension benefits because he hasn't worked the required 10 years in any one place.

Social Security thus stands alone as overwhelmingly the mainstay of the retired and disabled.

The system can be said to have fulfilled many of the hopes of its founders in providing income security to the aged in a systematic and guaranteed fashion, and it is enormous. Consider these statistics:

* In 1981 it had 36 million beneficiaries, of which all but 4.6 million were retired workers and their dependents or the survivors of deceased workers. The 4.6 million exceptions were severely disabled workers and their dependents.

* Total outlays in calendar 1981 were estimated as of Oct. 20 as $127 billion for retiree and survivor benefits, $18 billion for the disabled and $30.6 billion for the Medicare hospital insurance program. About $13 billion more was the estimated outlay for the Medicare out-of-hospital doctor-care program, which, unlike the rest of Social Security, is not financed from the Social Security payroll tax but from general revenues and premiums charged to beneficiaries.

* The maximum retiree benefit, paid to the worker retiring this month or next who has worked all his life at the highest wage subject to Social Security taxes, is $752.90. With a wife's extra "free" 50 percent benefit as well, such a worker would get $1,129 a month tax-free. However, average benefits are much lower: $383 for a retired worker and $413 for a disabled worker, plus the wife's benefit where applicable.

* The Social Security tax is 6.65 percent each for employers and employes, payable on the first $29,700 of income. On Jan. 1 it will rise to 6.70 percent, payable on the first $32,400. Although this means that the maximum tax will be substantial--$2,171 next year--and that for many workers Social Security is by far the biggest tax they pay, it should be noted that rates are even higher in many European countries, in some cases double.

With its huge size and essential social functions, the Social Security system is in serious financial difficulties, prompting disputes about whether it should be cut to keep costs down and thus ease the burden of future tax increases.

President Reagan, rejecting the alternatives of pumping in general revenues or raising the payroll tax beyond what is scheduled in existing law, last May 12 proposed a series of long-range cuts that, in effect, would have pared long-term benefits by over a fifth as compared with current law. Particularly big cuts would have been made in the basic benefit formula, disability benefits and benefits for those retiring at 62 instead of 65.

Unfavorable public reaction and attacks by Democrats forced Reagan to withdraw his proposals and ask for creation of a commission to seek a bipartisan solution.

The problems have three separate parts:

* Because of rising inflation in hospital costs, Medicare, which together with its charity counterpart Medicaid pays for about 36 percent of all hospital bills in the country, is going broke rapidly and permanently although it has a nice balance temporarily. If the economy goes fairly well, Medicare will be broke by the end of the decade if its share of the revenue from the payroll tax isn't changed from existing law. If the economy performs poorly, the breaking point will come by 1988.

Congress is already moving to pare Medicare benefits and costs somewhat, but it must do much more, or find some way to curb hospital-cost inflation, or pump in general Treasury revenues to meet the problem.

* The old-age and disability (OASDI) trust funds, taken as a unit, will run short of money in a year or so because the economy has performed very poorly over the past several years, thus producing higher cost-of-living benefits and lower revenues than projected. As new payroll taxes approved in 1977 kick in over the next decade, these funds will gradually recover and should have adequate balances until around the year 2020.

* But then the huge baby boom of the post-World War II era will start hitting retirement age and big, continuing OASDI deficits will develop, according to most demographic and economic projections.

The question that Congress and the president must address is how to tune the system into better long-term balance and where to find the money to meet the immediate crisis in the old-age and disability funds.

For the long term, suggestions include raising the basic retirement age from 65 to 68, increasing the penalty for opting for retirement at 62, decreasing the basic old-age benefit formula by 10 percent or so and paring away some of the dependents' and survivor benefits. Many Democrats and system loyalists believe many of these proposals, at least as laid out by the president, are far in excess of what is needed, and some prefer to pay for the added costs through general revenues or tax increases.

For the short term, there have been proposals for some benefit cuts, particularly in the annual cost-of-living adjustment. Many believe it puts too much pressure on the system and on the nation as a whole to have to pay full inflation increases each year, even when the economy otherwise is stagnating and the workers who are footing the bill through payroll taxes are themselves not keeping up with the increased cost of living in their wage scales.

So far, the bulk of Democrats in Congress have taken the position that the short-term crisis may be manageable by temporary borrowing from the Medicare fund, as long as it is flush, or from the Treasury, with the expectation that things will right themselves when the new revenues start rolling in during the later part of this decade.

However, new reports suggest that the margin of safety in borrowing from Medicare may be so slender that it would not do the trick adequately beyond the next two or three years, and not even that long if the economy doesn't improve over its current performance. That is about where Congress is at this moment.

If the nation concludes that the income security provided by the system is so valuable that it should not be cut at all and that the cost is worth it--some polls suggest this may well be a majority view--then the eventual solution to most of the problems probably will be higher Social Security taxes or use of general revenues from the Treasury.

Under current projections, it would only take an increased payroll tax rate of about 1 percentage point each on employers and employes, beyond what is scheduled under current law, to keep the old-age and disability trust funds snug for another 75 years if the economy goes reasonably well. Medicare is another matter.

But if the added tax burden seems too great, an era of paring may be underway.