The governors of Maryland and Virginia yesterday joined Washington area congressmen and Metro leaders to support special legislation in Congress that would provide enough money to finish the 101-mile Metro system.

Maryland Gov. Harry Hughes and Virginia Gov. John N. Dalton objected, however, to proposed language in one bill that would prohibit spending the construction money until "local participating governments have provided for a dedicated source of revenue" sufficient to meet Metro's mounting operating deficit.

Hughes called that provision "a difficult matter" and said that a method of funding operating deficits was under study in his state. Dalton said, "I oppose a dedicated state or local tax for reasons that rest upon a broad principle."

But Dalton also said that the state was working with Northern Virginia jurisdictions "on the formulation of a sound financial plan for continued Metro operations" and that such a plan could be in place by Sept. 30, 1980, "if required construction funding is authorized by Congress."

The letters from the governors were released at the end of the first day of hearings at the end of the first day of hearings by the regional affairs subcommittee of the House District Committee. Rep. Fortney H. (Pete) Stark (D-Calif.), subcommittee chairman, has offered a bill that would provide Metro with about $275 million annually in construction money beginning in fiscal 1982. That is in line with what the Carter administration is proposing.

Rep. Herbert E. Harris II (D-Va.), a member of the subcommittee, has a bill proposing $400 million annually, a figure more in line with what the Metro board has suggested.

The lower proposed amount would mean a two-to-three year extension-to 1989 or 1990-of the Metro construction program, General Manager Theodore C. Lutz testified yesterday. A third formula that would permit completion in 1987 or 1988 is also being considered.

Metro needs at least $1 billion more than is readily identifiable to complete the system. Area Reps. Harris, Joseph Fisher (D-Va.), Galdys Spellman (D-Md.), Michael Barnes (D-Md.) and Marjorie Holt (R-Md.) all spoke in favor of special legislation yesterday, as did Metro Board Chairman Jerry A. Moore Jr.

The administration has said that future Metro funds would be contingent upon the Washington area demonstrating that it could pay for operating the system with a "dedicated" tax.