Social Security old-age and disability insurance is the nation's single biggest problem, with about 35 million aged and disabled persons and their dependents receiving an estimated $103 billion to $104 billion in cash benefits in fiscal 1979.

When Congress increased Social Security taxes and cut long-range benefits in 1977, it believed that it had made the two cash-distribution programs secure and solvent for the next 50 years.

Most Social Security experts and actuaries still believe this is so, but the system faces several immediate vexing problems that will demand attention in the first months of 1980.

The first and politically most explosive of these is the drive on Capitol Hill, particularly the House, for a rollback of some of the Social Security payroll tax increases scheduled for future years by the 1977 legislation.

There is considerable feeling that the level of the payroll tax -- currently 6.13 percent each of employers and employes on the first $22,900 a year of wages and salaries -- is approaching the maximum politically permissible plateau.

As a result, many members have stated their desire to block new increases scheduled under existing law for Jan. 1, 1981, when the rate will jump to 6.65 percent and the maximum taxable wage reaches $29,700. It would be particularly attractive to block the increases because 1980 is an election year.

The question is whether this can be done without severe danger to the system or a sharp cutback in benefits.

Chairman J. J. Pickle (D-Tex.) of the House Social Security subcommittee put the issue most succinctly in a recent talk with reporters.

If Congress wants to hold the tax at 6.13 percent and slow up the automatic rise in the wage base in 1980, Pickle said, then it will have to come up with $14 to $15 billion a year in new revenues from elsewhere.

Cutting back some types of benefits may be possible, but it is politically inconceivable that any cutback could be of a scope sufficient to save anything close to $14 to $15 billion.

So most of the money would have to come out of general Treasury revenues, a prospect unattractive to many members of Congress who think it would simply mean shifting money from one pocket to another.

One possible way of shifting to general revenues to help ease the payroll tax impact has been proposed by the Social Security Advisory Council on the suggestion of Robert Ball, former Social Security Commissioner.

At present about 1.05 percentage points of the 6.13 percent tax goes to support the hospital insurance (Medicare) program. The council suggested that Medicare be funded entirely from general revenues, allowing the old-age and disability programs to receive all the revenues from the Social Security payroll tax. This would allow the latter to be reduced to 5.6 percent overall until the year 2005 when it would go up to 7.5 percent which still would be less than the total rate for the period scheduled under present law.

Whether the Carter administration recommends something along these lines for 1980 action may well depend on the overall condition of the economy toward the end of this year and into the start of 1980. If the economy lags to the point where President Carter's advisers want a tax cut to stimulate it, it is possible that they would want to make the cut take place in the payroll tax on grounds this would help reduce inflation more.

So far, however, Carter's advisers have been saying that an economy stimulating tax cut isn't called for yet. Moreover, there are hints from a variety of places in the administration that if a tax-cut is recommended, they may end up after all seeking an income-tax cut.

A second problem for Social Security financing is that the economy hasn't been performing nearly as well as anticipated in 1977. Inflation has meant higher benefits (benefits are automatically indexed for cost-of-living rises) while slowdown will mean higher unemployment and therefore less payroll tax income.

As a result, according to the congressional Budget Office and other economic forecasting units, there may be a temporary cash shortfall in the early 1980s, before new revenues voted in 1977 accumulate sufficiently to meet needs. The CBO estimated that the old-age trust fund could dip in 1984 to a reserve of only 5.4 percent of estimated cash benefits for the year, not enough to assure cash-flow needs at all times.

There is widespread agreement that the old-age fund could meet this problem if it is allowed to borrow temporarily from the disability fund, which is more flush, or the Treasury.

This is the solution favored by the Department of Health, Education and Welfare and by the Advisory Council. But many on Capitol Hill are reluctant to allow such borrowing or exchanges, fearing it could become endemic or could become a system for permanent, unrepaid drains on the Treasury. Legislation will be required to allow the exchanges.

The shortfall problem -- and the dislike of borrowing by many fiscal conservatives -- will be one factor mitigating against the drive to roll back Social Security taxes. With the short-term balance so precarious, it would be dangerous to roll back the tax unless there are absolute assurances of alternative financing.

One way out of this dilemma would be to cut benefits. If benefits were reduced, then the financial condition of the system could be strengthened and taxes held down somewhat over the years, according to some thinkers.

A move somewhat along these lines already has been suggested, in different form, by the Carter administration and some GOP members of the House Ways and Means Committee.

In its budget a year ago, the Carter administration proposed paring down what it considered to be a pack of marginal benefits, not basic to retirement and disability protection, which had crept into the system over the years but were no longer justified.

For example, it proposed cuts in the level of monthly disability benefits for families; eliminating the $255 burial benefit and cutting off a child's dependent or survivor benefit at age 18 instead of letting it continue until age 23 if the child is a student.

The package would have saved only $600 million to first year but by the middle 1980s the figure would have been several billion. Stanford Ross, Social Security commissioner who has just announced that he is quitting to return to private law practice, said last week that these kinds of cuts are necessary to ease financial burdens on the system and thus assure that the essential, basic care benefits will survive unharmed.

However, former HEW Secretary Wilbur J. Cohen and Ball violentl opposed these cuts and put together a huge coalition of organizations of the elderly that easily blocked action on everything but the disability bill, which has passed the House and the Senate Finance Committee.

Cohen and Ball argued that the proposed cuts are too great and go far beyond what is needed to protect the system. Except for disability, which is well advanced in the legislative process, the Carter administration may well draw back from really pushing these proposals this year for fear of consequences in the election from the coalition of the elderly.