IT'S ALMOST A LAW of American politics, enshrined in the lore of Capitol Hill operations, that a federal program survives and grows fat when the money is spread around liberally, not limited to some tiny constituency.

So perhaps it is no surprise that a little program, which began in 1961 by dishing out development aid to businesses and governments in "depressed areas" of Appalachia and small-town America, now counts nearly 85 percent of the country's population as being in "distressed areas" eligible for help.

Sen. William Proxmire of Wisconsin, often critical of federal aid programs, outdid himself on the eligibility issue when the measure -- now called the Public Works and Redevelopment Act -- reached the Senate floor for its new authorization last year.

"Get this -- 84.5 percent of the population eligible for assistance. 84.5 percent! That is ridiculous. It is a joke," he shouted. "I do not know how you can run a reasonable economic development program if you have to define 84.5 percent of the population as eligible and as living in distressed areas."

How you do it is really no mystery, as Proxmire surely knows. You take a program created in the 1960s with a modest $90 million or so a year to give to a limited number of poverty pockets. In 1966, for example, eligible areas had a total population of about 29 million, according to an Economic Development Administration booklet published by the parent Commerce Department.

Then you start to diversify until, according to department estimates and statements on the House and Senate floors, nearly 2,500 of the nation's 3,000-odd counties now meet the program's unemployment and poverty criteria -- areas with an estimated population of nearly 190 million.

That will make you beloved among members of Congress from coast to coast. Last year's congressional debate gives the flavor of just how much the EDA is appreciated for the nearly $1 billion a year in grants, low-interest loans and loan guarantees it now disburses -- while others have a far tougher time getting a similar, if larger, loan guarantee for an ailing Chrysler Corp.

"In my state of Arkansas," Sen. Dale Bumpers declared, "the EDA has spent on the average of $6 million a year over the past 10 years for more than 200 projects. In fiscal year 1979 it will spend in excess of $7 million." Then he lauded EDA as "responsible, flexible and supportive of grass-roots decision-making."

Sen. Harrison A. Williams of New Jersey sang the praises of an EDA guarantee of a $12 million loan to help the Raritan Steel Co. build a mini-steel mill at Perth Amboy.

Sen. Jennings Randolph, chairman of the Senate committee with jurisdiction over the program, ticked off a list suggesting that the hollows of his state of West Virginia are paved with EDA-financed industrial parks. His wife's hometown of Keyser obtained an industrial park and water and sewer facilities. Charleston got a civic center. Fourco Glass Co. in Clarksburg and Rockwell in Morgantown received loan aid. And so on.

In the House, Rep. Robert Roe (D-N.J.), who piloted the measure there, called EDA operations "a very cost-effective way for the federal government to address structured economic problems and the attendant unemployment."

Rep. Don Clausen (R-Calif.), not exactly among the liberal, big-spender types, asserted, "I have seen firsthand the revitalizing and stabilizing influence EDA projects have had on many of our communities and counties. The counties of Sonoma, Mendocino, Lake Humboldt are the recipients of substantial benefits from the program."

Not only is the program now virtually coterminous with the entire country, but it is getting into some pretty big enterprises, especially through the Chrysler-like loan guarantee route. EDA has guaranteed $83 million in loans to help Sea Train build commercial ships in the Brooklyn (N.Y.) Navy Yard in order to create jobs after the Navy closed its operations there. Under a special program, it has reserved a $100 million loan guarantee for construction of a new steel plant in depressed Youngstown, Ohio. And it is providing another $100 million guarantee to help the Wheeling-Pittsburgh Steel Corp. build a plant to produce extra-long train rails in Monessen, Pa.

It should surprise nobody, then, that the something-for-almost-everybody measure cleared the Senate by a margin of 83 to 17 and the House by 301 to 99 -- with EDA's grant, loan and loan-guarantee authority expanded to more than $3 billion. This was done at the urging of President Carter, who was impressed by an urban task force recommendation for the expansion, with most of the increase targeted for business loan guarantees in urban areas.

"The idea was that the Farmers Home Administration and some other agencies provide rural business credit, so EDA would have to become the main agency for business loans and credits in cities," says one administration official." All from a little program created for Appalachia and small-town America.

Everything, of course, has not been entirely clear sailing for the EDA program. The Senate version of the measure, at the administration's request, cut eligible areas to those with "only" 67 percent of the country's population. The House version, however, boosted the figure to 90 percent, and the two bills have yet to be reconciled in a House-Senate conference.

Moreover, the inflation crisis has caused Carter to pull back a bit, and the extension, along with many other measures, has been slowed in Congress because of the current battle of the budget. But Carter is still asking a program level of $1.7 billion for fiscal 1981 -- an increase of about 80 percent from fiscal 1979. (The 1980 program level is still uncertain because of last-minute budget changes.)

There is, in addition, the larger question to be asked: Has the program really done that much good?

Assistant Secretary of Commerce Robert Hall, who administers the program, believes it unquestionably has. The idea, he stresses, is not just to hand out some money that has a temporary impact and is gone. It is to put the money where it will promote the growth of industry and the creation of permanent jobs in the private sector.

EDA figures it has created lots of permanent jobs. Since 1965, according to its count, it has committed about $4.1 billion, chiefly in "infrastructure" grants -- for sewer and water systems, industrial parks, access roads, ports, terminals and other facilities that attract private business -- but also for loans and loan guarantees.

In return, it figures, it has saved or created about 445,000 permanent jobs. If its numbers are correct, that would come to a cost of about $10,000 per job -- a pretty good buy. And losses so far on loans and loan guarantees have only been about $55 million.

It has books loaded with success stories. South Bend, Ind., lost 7,000 jobs when Studebaker, the auto maker, shut down, but EDA helped it get new businesses. The Mohawk Valley in New York lost old decaying industries but found new ones. Prosperity ended in Pryor, Okla., when a government ordnance plant shut down, but EDA helped finance an industrial park that brought in new businesses.

Still, there are nagging questions. Whether the job-creation figures are sound is one of them. Proxmire's criticism, endorsed by such others as Sen. John Chafee of Rhode Island, is another: When everyone is eligible, some of the precious dollars are bound to be frittered away on low-priority projects.

This is especially so, as James Lynn, a former Cabinet member in the Nixon-Ford administration, puts it, when "political pressures . . . become intense" from powerful congressmen pushing to have projects in their areas jumped to the head of the list.

One former EDA official says that a top aide to President Johnson used to call regularly and press EDA officials to speed projects for powerful committee chairmen. And another former Nixon-Ford aide says that when the Office of Management and Budget held up projects sought by influential members of Congress, "We'd go and pound on OMB director Roy Ash and say, 'Are you going to destroy all our influence up there for a crummy little sewer project?'"

The most basic question, however, is whether, with all its statistics of success, EDA really promotes a net job growth in the economy. Some observers think that in the long run, it merely shifts jobs and capital from more prosperous to less prosperous sections -- good for those who win, bad for those who lose.

Legally, EDA has to avoid projects that foster pirating of jobs from one area to another. But in practice, critics say, it's often not evident that this is happening. You have a big factory in New York and a small one in North Carolina. You want to build an extra plant and can do it in either state. If EDA helps North Carolina build you an industrial park and sewers and then gives you a low-interest loan, why not go there? A few years later, you might even close your New York plant.

Early on, for example, EDA helped depressed Oakland, Calif., build a containerport to handle more ocean freight. EDA boasts that this created 3,000 permanent jobs. Great for Oakland. But according to a spokesman for Diane Feinstein, the mayor of San Fransico, not so good for Frisco, which lost shipping business to Oakland. "It helped Oakland; it hurt us."

Lynn says that some Nixon administration officials, concluding that EDA ultimately just shifts growth "from one place to another" without adding much to the overall economy, favored killing the program. In 1973 Nixon vetoed a bill extending it and said, "I am convinced that this program has done little to help the poor." But he was overruled by Congress.

Assistant Secretary Hall, of course, doesn't agree with the critics. "I believe there is net economic growth in the country as a result of this program," he says, asserting that he expects a new study now under way to demonstrate this.

Hall concedes that not every project can be successful, but he contends a good percentage are. In the Oakland case, for example, he says the Port of San Fransisco had built itself a new bulk cargo system unable to handle container cargo, and, moreover, didn't have enough space available for a large containerport. So even if the Oakland facility hadn't been built, San Francisco would have lost business to other West Coast containerports, he contends.

He also says that criticism of the Wheeling -Pitt plant -- asserting that it will merely create excess train-rail capacity -- is misplaced. Existing steel facilities can't produce extra-long rails at internationally competitive prices, Hall says, while the new one can, so it's not merely "excess capacity."

But despite the nagging doubts, a year ago it looked like the original Carter-requested expansions would be enacted easily. Since last year, the inflation crisis has brought demands for a budget shrinkage, especially in government credit programs, and that may prove an obstacle to the big enlargement of loan guarantees sought by Carter. But, if the inflation crisis clears, these problems could disappear. The EDA program has, without doubt, an extremely grateful constituency on Capitol Hill.