Congress opened hearings last week on a matter vital to 2.8 million Social Security beneficiaries: Should the government restore the minimum benefit payment cut out of the budget last month?

If that payment is not restored the government will save about $1 billion a year. The flip side of saving all that money is that, starting with the April check, Social Security minimum benefits will decline. This cut affects people already on the Social Security rolls, not just future beneficiaries.

The Social Security subcommittee of the House of Representatives agrees with the president that future beneficiaries should be cut, but wants to keep checks coming to all the people already getting them.

The minimum benefit was designed to protect people who worked under Social Security coverage but contributed only small amounts. Many years ago, for example, you or your late spouse could have contributed a maximum of only $100 or $200 a year to Social Security and maybe less. If benefits were figured strictly according to what was paid, you might get only a few dollars a month.

Under today's high wage levels, full-time workers will automatically receive more than the minimum benefit. So for most current employes, the minimum-benefit question is moot. The administration argues that it is also moot for most of the people now on the Social Security rolls. Of today's 2.8 million beneficiaries, many would or could pick up in other Social Security benefits whatever they lose from their minimum benefit check. In fact, the administration says only 300,000 people would actually lose benefits, and claims that most of these people have other sources of income.

The Wall Street Journal editorialized that those being cut off are merely "double dippers" (that is, people who also have federal pensions) and coupon clippers.

But are they really? The House subcommittee thinks that more people might be hurt than the administration claims, especially people who are poor but proud. Figures from the Social Security Administration suggest that at least 1.5 million people now getting minimum benefits would be fully protected from any cuts.

That includes about one million spouses, mostly married women or widows, who earned little during their working years. What they lose in minimum benefits they will pick up in benefits due them on their spouses' accounts. Another 500,000 are on the old-age welfare program called Supplemental Security Income. SSI will pick up their minimum benefit losses, probably dollar for dollar. What happens to the other 1.3 million minimum-benefit beneficiaries is an open question. According to the House subcommittee, they include:

* 200,000 students, most of whom have lost at least one parent. Students who lose Social Security benefits may, or may not, qualify for larger goverment education grants.

* 600,000 elderly people, the great majority of them women, who will be eligible for SSI welfare payments. In truth most of these people are already eligible for some SSI payments, but have not joined the program. They resist, mainly because of the stigma of welfare. If benefits are cut, it is simply not known how many of these proud, elderly poor would be driven to SSI and how many would continue to resist.

* 360,000 double dippers, not all of whom will be cut off. Take, for example, a woman who gets both a federal pension and a minimum Social Security benefit, and whose husband also gets Social Security. Whatever she loses on her minimum benefit, she may gain as a spouse on her husband's Social Security account.

* An estimated 140,000 people who aren't eligible for compensatory SSI payments, because they have more than $1,500 in savings ($2,500 for couples) or earn more than $65 a month. Veterans benefits, workers compensation and company pensions could also disqualify you from SSI.

By this count, those most severely hurt will be the elderly poor who are too proud to apply for welfare or whose marginal jobs disqualify them for SSI. You (or your elderly parent) may be receiving the minimum Social Security benefit without realizing it.

The base amount is $122 a month. But annual cost-of-living increases have raised that sum for most people.

The average payment is now about $150 and could be $20 higher. The average cut is expected to be about $70 a month -- leaving the average affected beneficiary with $80 a month from the Social Security system (and possible much less). If you had low earnings under the Social Security system, you really can't tell whether you'll be affected by this cut until you get your April check -- or until Congress decides to leave the minimum benefit alone.