A higher federal payment for the District of Columbia, proposed yesterday by Mayor Walter E. Washington, faces an uncertain and even hostile reception on Capitol Hill, with one key senator declaring himself firmly opposed.

The mayor said the city will seek a federal payment of $317 million in the 1979 fiscal year, which begins Oct. 1, 1978, requiring a change from the existing law that sets a lid of $300 million.

The federal payment is the money the government pays the city each year chiefly to compensate for untaxed federal properties.

Sen. Thomas F. Eagleton (D-Mo.), chairman of the Senate Governmental Affairs Subcommittee on the District, which must pass upon any authorization for a higher payment, issued a statement yesterday saying he "will oppose any increase . . . until the District government has demonstrated considerably greater efficiency in spending the money it now gets."

Eagleton said the city should not costs by reducing its payroll below the approximately 36,000 it now employes, a level he called "higher than any comparable jurisdiction."

Rep. Charles C. Diggs (D-Mich.), chairman of the House Disrict Committee, which also must pass upon a higher payment, was in Detroit yesterday and could not be reached.

Although it would take action by both chambers of Congress to approve an increase, either chamber could block it. If history offers a guide, it would be nearly impossible to win Senate approval of an increase without Eagleton's support.

Eagleton already has an ally in Sen. Patrick J. Leahy (D-Vt.), chairman of the Senate District Appropriations Subcommittee an a fiscal conservative who is seeking a hold the line in fiscal 1978 on a federal payment of $276 million, $24 million less than the authorized maximum.

Three months ago, Leahy informed Vice President Mondale, chairman of a White House task force on D.C. affairs, that he thinks the federal payment should be based not only on the city's cost of operations, but also on a clear accounting of the services the city provides in return to the U.S. government.

This, Leahy noted, is required by the city's 1973 home rule charter, and has not been done to his satisfaction.

In calling for the $317 million payment, Mayor Washington said this amount had been approved by the U.S. Office of Management and Budget as a target figure for city financial planning.

Yesterday's exchange underscored the continued dominant role the federal government plays in District affairs, despite home rule.

Before it goes into effect, the budget submitted by the mayor must go through 13 more basic administrative and legislative steps - three within the District government, three at the White House and seven in Congress.

When finally approved, the budget will take the form of a federal appropriation law, the same kind of law Congress must pay to supply funds for the Pentagon and the State Department.

The measure will now be the subject of City Council committee hearings, enactment by th full Concuil, approval (or disapproval) by the mayor of the Council version, screening and approval by OMB, then submission by the President to Congress. That will come early next year.

On Capitol Hill, three steps are taken by each chamber of Congress (subcommittee action, committee action, floor action, followed by a joint conference committee to resolve differences. Then the measure goes back to the President for signature.

The process is so complex that the budget for the 1978 fiscal year is now only halfway through Congress. Rep. William H. Natcher (D-Ky.), chairman of the House District Appropriations Subcommittee, blamed OMB and the city government for a delay in submitting their proposals.