The jobless, the homeless, the sick and the helpless in search of emergency aid are turning in growing numbers to private nonprofit organizations. Many of the needy have been wrung out of federal and state programs because of budget cuts. Others are recession victims.

They are washing up on the steps of churches and charity soup kitchens, at the doors of privately run shelters and hospital emergency rooms, seeking food, clothing, medicine, help with the fuel bills or a roof for the night.

Yet just when the poor most need the help of private charities, the private charities have less to give. o a far greater extent than most Americans realize, private nonprofit organizations depend on federal funds. In 1980, voluntary organizations received $40.4 billion from the federal government, compared with $25.5 billion from all private sources, including individuals, corporations and foundations.

And this all-important federal funding is being cut. Under the fiscal 1982 budget, private organizations will lose an estimated $33 billion between 1982 and 1985, according to The Urban Institute. President Reagan hopes that private giving will fill the gap. But the dollar lost to private charities is far too large for individuals to overcome.

During fiscal 1982 -- the first year that federal budget cuts began to bite -- many charities managed to maintain programs at the same level. They did it by appealing desperately to their traditional donors and by mailing fund-raising letters detailing the need to replace lost federal funds.

But holding programs at the same level means a real reduction in services, after adjusting for inflation. And the new clients banging at the doors may have to be turned away.

Generous as many Americans are in their private giving, it seems likely that the growth in donations will decline. Corporations gave approximately $3 billion last year to nonprofit institutions, but corporate donations follow profits and profits have been poor. Preliminary surveys by The Conference Board suggest that corporate giving is slowing down.

Individual giving may also slow, especially among the wealthy. The Reagan tax cuts left higher-income people with more money to give -- but the tax cuts also reduced the tax incentives that lie behind many deductible contributions. There are now more incentives to save or invest than to give money for relief of the poor.

Even if private giving goes up, it may not necessarily benefit the same organizations that are losing federal funds. Hospitals, for example, are facing cutbacks in Medicare and Medicaid payments. Reduced federal support will limit the amount of free care that can be dispensed through hospital emergency rooms. Good private hospitals are a traditional object of charity for corporations and wealthy families. But municipal and county hospitals, where most of the poor wind up, depend more on tax dollars -- and those dollars are limited.

Churches always gain from any increase in private giving. More than half of the $44.5 billion given last year by individuals went into the collection plate. Yet the churches most called on to help the poor are those located in poor neighborhoods whose parishioners have little money. Wealthy churches have fewer burdens.

Social-welfare organizations face the severest budget cuts -- especially those organizations that fund job programs, day-care centers and other projects that piggybacked on federal funds. Some of these groups can turn to a few wealthy individuals who care about their causes. But as a general rule, these charities don't attract the attention of the average giver.

Nor do they appeal to corporations. President Reagan is asking corporations to increase their charitable donations. But the Boy Scouts or a symphony orchestra is more apt to be the beneficiary of corporate largess than a struggling day-care center for the children of welfare mothers seeking work.

It would be nice to believe that individuals, especially the rich, will increase their charitable giving this year and every year in the future. But even if they did, they cannot hope to fill the gap left by decreased federal funding.

As government aid to nonprofit groups declines, the impact and reach of private charities will also decline, just when the poor and the homeless need help most.