Ronald Reagan's budget-cutters are following a well-worn path filled with political landmines by proposing to dismantle the Appalachian Regional Commission and the Economic Development Administration, two of the most resilient legacies of John F. Kennedy's New Frontier and Lyndon B. Johnson's Great Society.

Richard M. Nixon tried to get rid of both programs almost a decade ago and failed miserably. He found taht despite the low profiles of the two agencies and their all-but-forgotten mandates, both have very powerful friends. The reason: both dispense a great deal of pork -- not just to the poor but to states, local governments and businesses.

The political allies of the two programs have always been extremely well-placed. Two of the Appalachian program's biggest clients, for example, are the states of West Virginia, home of Senate Minority Leader Robert C. Byrd, and Tenneessee, home of Senate Majority Leader Howard H. Baker jr.

As the Senate Republican leader, Baker has pledged to fight for Reagan's entire economic program. But politicans have a habit of blinking when issues get close to home.

"The senator is totally committed to getting the president's program throuh," a Baker press spokesman said yesterday. "But he isn't going to sit on his hands and have his state suffer more than any other state."

Baker and Byrd aren't alone. Appalachia, as defined by the ARC, includes 13 states from New York to Mississippi. This gives the commission a ready-made constituency of 13 governors, 26 senators and scores of represenatives. The EDA, begun as a rather modest program to aid severely depressed areas, now considers where 85 percent of the country's population lives a "depressed area," giving it an even broader base.

Sen. Jennings Randolph of West Virginia, the ranking Democrat on the Senate Environment and Public Works Committee, refers to David A. Stockman, director of the Office of Management and Budget and the chief architect of the budget cuts, as "sock 'em," and predicts he will have little luck eliminating EDA or ARC on Capitol Hill because "these programs have broad support."

"I can't believe President Reagan himself will take the advice of this 'sock 'em' fellow," says Randolph, who authored legislative creating both agencies in 1965. "This is a meat-ax approach. It ignores everything we've accomplished. I will support reasonable budget cuts. But this is unrealistic and unreasonable. In fact, it is tragic."

These are, of course, fighting words.

Reagan's budget-cutters may be more successful than Nixon's. But they are using essentially the same arguments against EDA and ARC that Nixon's budget-cutters did almost a decade ago. On the surface, the arguments are convincing.

OMB Director Stockman's big black book of budget cuts argues that the Appalachian commission should be eliminated because "ARC's impact on reginal or subregional conditions is not identifiable."

The book goes into more detail on EDA. It argues that the Reagan administration will rely on tax cuts, reducing government regulations and an improved economy to stimulate business expansion. It charges that most of EDA's loans have gone to large corportaions, that it hasn't influenced plant locations and that its programs are not cost-effective. It claims the agency spends from $40,000 to $50,000 creating one job for one year -- a figure EDA officials say is a gross exaggeration.

"Evidence seems to indicate that EDA funds have little impact in creating net new jobs and capital investiment in the national economy," the black book says. "Under EDA's existing legislation, over 80 percent of the nation's population lives in areas eligible for EDA aid. Consequently, EDA resources have been widely distributed, often in subcritical amounts; targeting to neediest areas has not been achieved; and job creation has been difficult to prove."

Sen. William Proxmire (D-Wis.) cited similar figures the last time EDA came up for congressional extension in 1979. "This is ridiculous. It is a joke," he shouted on the Senate floor. "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."

But few members of Congress were impressed. The something-for-almost-everyone measure cleared the Senate by 83 to 17 and the House by 301 to 99.

By Washington standards, the EDA and ARC are small pototoes. Carter's fiscal 1981 budget called for $668 million for EDA, $343 million for the ARC, and $44 million for nine other regional commissions that Stockman would also like abolished.

EDA and ARC are outgrowths of the old Area Development Administration -- part of Kennedy's New Frontier -- and public concern in the early 1960s over poverty and distressed areas, particularly in the mountain regions of West Virginia, Pennsylvania and Kentucky. Both were created with great fanfare in 1965 as part of Johnson's War on Poverty. w

EDA's goal is to reduce persistent unemployment in chronically distressed areas by providing loans and grants to businesses and local governments. The ARC has a similar goal in the Appalachian region, providing money for highways, vocational schools, medical clinics and a host of other programs. It is a federal-state agency that attempts to shift decision making away from Washington to states and local development districts.