In June the Reagan administration came out with an idea designed to reduce government paperwork, cut the size of the bureaucracy and reduce the deficit by at least $100 million over the next five years.

Just what everybody wants, right?

Wrong. Since the administration released its formal proposal for a swap of 34 million acres of federal land between the Interior Department's Bureau of Land Management and Agriculture Department's U.S. Forest Service -- a plan that would eliminate overlapping jurisdictions in 13 western states -- politicians and private citizens throughout the region have been denouncing the idea.

After touring the western states last month, Interior Secretary Donald P. Hodel concluded sadly that the land swap plan demonstrates an old rule of government: "Everybody wants to reduce the federal bureaucracy until you start talking about doing it in their back yard."

At a conference on the exchange plan held here last week by Outdoors Unlimited, a coalition of public-land users, an unlikely combine of ranchers, miners, oil executives and environmentalists agreed that the land swap should be shelved.

And it probably will be. Despite their repeated calls for new ways to reduce the deficit, western members of Congress have lined up strongly against the exchange, which requires congressional approval.

John Moeller, BLM director of management resources and an architect of the proposed land swap, said the agencies will go ahead nonetheless and present a final proposal to Congress this fall.

But Moeller concedes that a public comment period this summer was not propitious.

Nobody challenged the basic idea of a land swap. As Moeller puts it, "Who could be against improving service, reducing inefficiency and cutting government costs?" But well over 90 percent of the comments received on the plan were negative, taking issue with some specific aspect of it.

This response was not entirely unpredictable. For about five decades, the Interior and Agriculture departments have been looking for ways to combine the operations of their big public-land-management arms, the BLM and the Forest Service.

There have been several plans to merge the agencies -- the most recent was the proposed "Department of Natural Resources" during the Carter administration. But all have fallen before the political onslaught of groups unwilling to change the status quo.

By historical standards, the Reagan administration plan to keep two separate agencies but redraw the boundaries of the land parcels they administer is relatively modest. The plan would shift about 18 million acres of BLM land to the Forest Service and 16 million acres of Forest Service land the other way.

As a general rule, the exchange is designed to replace the current patchwork pattern of alternative management responsibility with large contiguous blocks of land under a single agency.

Under the swap, for example, the Forest Service would take over BLM holdings east of the Mississippi, while the BLM would take over the other agency's land in North Dakota. At present, both agencies have many tracts of land in each area.

That has led to considerable duplication: two sets of maps, two recreation policies, two sets of bureaucrats to run contiguous blocks of land with quite similar geology and topography.

There are 71 towns in the western states where both agencies maintain offices to manage the surrounding land. The exhange would reduce that to 22 towns, so 49 redundant government offices could be closed.

For the government, this would mean cutting 700 to 800 jobs, the agencies say, and annual savings of $30 million or more. Subtracting the $45 million it would cost to implement the swap, that means net savings of $105 million or more in the first five years.

For the public, the agencies argue, the swap would mean "one-stop shopping" for the maps, permits and so forth needed to use federal land -- in addition to budget savings.

Somehow, though, these potential benefits have been outweighed by what BLM Director Robert F. Burford calls "the turf-protection instinct."

Many public land users -- miners, grazers, hunters, hikers -- have become comfortable over the years with the existing manager of the lands they use, be it Forest Service or BLM, and they are resistant to change.

Environmentalists in Wyoming, for example, complained bitterly about the proposed transfer of Big Horn National Forest to the BLM. They said the bureau would show less concern for conservation needs than the Forest Service. But Colorado ranchers, who have learned to live with BLM management of grazing land, said a transfer to Forest Service control could mean more restrictions for them.

As a result, many involved in the issue -- including agency officials -- say that the effort to make the exchange is an exercise in futility. At the conference here, Philip Hocker, national treasurer of the Sierra Club, declared, "There's a very simple four-letter word to describe this proposal: D-E-A-D."