The Agriculture Department's Soil Conservation Service, one of the most politically popular farm programs in history, would be abolished under administration budget officials' plans to reduce the federal deficit.

But Agriculture Secretary John R. Block, according to sources, is appealing to President Reagan to overrule the Office of Management and Budget proposal, which would chop the SCS fiscal 1986 budget to around $350 million from its current level of about $821 million.

These sources added, however, that Block's task is made more difficult because soil conservation is just one of a number of USDA programs that he is defending from OMB Director David A. Stockman's pruning shears.

Should Stockman prevail, Block likely could count on strong support from SCS advocates on Capitol Hill and from soil conservation and farmer organizations in his effort to save the 14,000-employe agency.

Since 1981, when the Reagan administration began proposing SCS budget cuts, Congress routinely has restored funding and pushed for more programs. Only a hard-line stance by the administration last summer prevented Congress from approving a major broadening of existing programs.

Under the new OMB proposal, the SCS would use its fiscal 1986 funds to honor existing technical service contracts and then begin shutting down its nationwide network of technical-support offices in virtually every county in the United States. Sources said this would mean dismissing thousands of SCS employes here and across the country.

USDA officials were reluctant to comment yesterday on Block's appeal, still pending at the White House level. But they said the secretary would accept a freeze on agency spending at 1985 levels or would go along with a 10 percent cut that has been discussed for all federal agencies.

The bulk of the SCS budget is directed toward providing on-farm technical assistance in controlling soil erosion and in adopting tillage practices that preserve topsoil.

Beyond that, the SCS is involved in a variety of soil and water programs in rural areas. It helps develop small-watershed flood controls, conducts surveys that help determine erosion and fertility problems, and inventories cropland. In mountainous areas of the West, its annual snow surveys help avert flood damage through regulated release of runoff from impoundments.

These programs over the years have acquired strong congressional patronage and administration efforts since 1981 to chip at them largely have been unsuccessful.

One of the programs promoted by Block and Peter C. Myers, the Missouri farmer who heads the SCS, would target USDA technical assistance for erosion control at the hardest-hit areas. But in the battle over USDA's fiscal 1985 budget, after the administration sought $475 million for the SCS, Congress restored $346 million of proposed cuts and barred the SCS from further targeting.

The announcement last week that Myers would be nominated as assistant secretary for natural resources and environment is viewed by conservationists as another sign that the SCS would be downgraded. Myers, if confirmed by the Senate, would succeed John B. Crowell Jr., who resigned.

Soil preservation groups have given Myers generally high marks for his work at the SCS, although his appointment in 1982 was denounced bitterly because he was the first nonprofessional to head the agency. It was created as a result of public alarm over the Dust Bowl disaster of the 1930s.