Critics of the proposed convention center in downtown Washington sought without apparent success yesterday to dissuade Rep. William H. Natcher (D-Ky.) from his announced support of the $110-million project.

The critics, appearing at a public hearing of the House District Appropriations Subcommittee, which Natcher heads, did, however, pick up an outspoken ally from its membership, Rep. Gunn McKay (D-Utah).

For too long, McKay said, Washingtonians have sold Congress on the notion that taxpayers across the land should spend money on projects to enhance Washington just because it is the nation's capital.

"Well, we need a Metro, I suppose," McKay observed, citing the region's biggest federally assisted project, "but how many (such projects) can we afford in the name of a national center?"

McKay's comments reflected a common misunderstanding about the convention project's financing. The city is proposing to pay off the entire $110 million (plus interest) from future municipal revenues, composed mostly of local taxes supplemented by the annual federal payment to the city.

The subcommittee is considering the District's request to let it borrow $27.7 million from the U.S. Treasury during the 1978 fiscal year to plan and start buying three blocks of land for the center.

Ultimately the city would borrow the entire $110 million. In a few years, city officials hope to refinance the project by floating municipal bonds and repaying the Treasury out of the proceeds.

The center site is on the south side of New York Avenue between 9th and 11th Streets NW, in the seedy Mount Vernon Square area.

Nat hatcher usually gets hiw way on the subcommittee. He did not respond to McKay's attack on the convention center, or to hostile comments about it by witnesses.

After opposing an earlier version of the center a few years ago, Natcher voiced full support for the revived project at a hearing Wednesday at which District officials testified in favor of their proposal.

Yesterday, private citizens and groups had their say, and the testimony was mixed and familiar. Most had already testified at a hearing held two weeks ago by the Senate District Appropriations Subcommittee, whose chairman, Sen. Patrick J. Leahy (D-Vt.), is skeptical about the center.

Eight witnesses, chiefly representing business interests, favored the center yesterday. They asserted that it would have such "spin-off" benefits as the construction of hotels containing 3,000 rooms, the creation of 4,000 full-time jobs and increased tax revenues that would produce a net profit of $12 million a year to the city treasury.

Thirteen witnesses, chiefly representing neighborhood citizen organizations, opposed or criticized the center. They contended the city's projections are too rosy.

John J. Phelan, an economist, speaking for the Capitol Hill Restoration Society, said his calculations indicate that the center, at best, would provide only 1,700 jobs.

Kathy Lipscomb, coordinator for the Dupont Circle Advisory Neighborhood Commission, an official city-created body, contended that the City Council violated a law by giving insufficient notice of its hearing on the center proposal, which resulted in a Council decision to endorse the convention center funding.

Lipscomb disclosed that the city's top legal officer, Corporation Counsel John R. Risher Jr., agreed to review the Council's procedure. Risher said yesterday that the review has not been completed.