The Virginia House of Delegates Appropriations Committee today included $10 million for Metrorail construction aid in a bill that also proposes to balance the state's current biennial budget without a tax increase.

The $10 million appropriation to Metro from state gasoline taxes was vetoed by Gov. Mills E. Godwin last year when the current two-year budget was adopted. Northern Virginians tried unsuccessfully to overturn the veto in the state Supreme Court.

The money was again inserted in the budget bill during closed sessions of the Appropriations Committee last week. Members said there was no controversy over the item when Del. James M. Thomson (D-Alexandria) offered it. Some members said that any opponents of the Metro appropriation probably assume it will die in the Senate or be vetoed again.

Sen. Adelard L. Brault (D-Fairfax), Senate majority leader and a member of its Finance Committee, said in an interview that the Metro funds "will have a tough time in the Senate."

Sen. Edward E. Willey (D-Richmond), chairman of the Finance Committee and a post opponent of Metro funding, said, "I feel very sorry for the people in Northern Virginia who are saddled with this thing and I don't want to start waving any red flags. But I don't see how the state can get involved in trying to bail that project out."

No effort was made in the Appropriations Committee, to rewrite the Metro item in a way that would insulate it from separate veto by Godwin. The language appropriating the money, $5 million in each year of the biennium, is identical to the language vetoed last year.

Some Metro funding advocates are clinging to the hope that Godwin has changed his attitude toward the rail project, which he once called a "boondoggle." U.S. Secretary of Transportation Brock Adams said last week that Godwin "has indicated to me his full support" for completing the entire Metro system in Virginia.

When asked to confirm this, however, Godwin said through an aide that his policy on Metro has not changed since he wrote a letter on Jan. 13 to Adams' predecessor, William T. Coleman Jr., accepting federal conditions for the construction of Interstate Rte. 66 in Arlington. In that letter, Godwin emphasized that he could make no commitments on behalf of future state governments, and he promised no more than the $75 million in construction aid to Metrorail that will flow from the 1-66 agreement with Coleman.

The proposed Metro funds are already earmarked for transit aid and, if not directed to Metrorail construction, will revert to a fund controlled by the Highway and Transportation Commission and used primarily to help cities and counties buy buses.

The amendments to the state's $3.6 billion general fund budget reported by the Appropriations Committee express the consensus of the House of Delegates that the $102 million revenue shortfall by July 1978 should be closed without a tax increase. All 100 House members are up for re-election this year.

However, not all delegates believe the Appropriations Committee approach will solve the state's revenue problems. Del. Carrington Williams (D-Fairfax), chairman of the state Revenue Resources Commission and a member of the House Finance Committee, immediately criticized the budget proposal.

An essential part of the plan is a speedup in sales tax and income tax collections that will provide a one-time, $40 million increase in tax collections next year. As the Finance Committee approved these speedups today, Williams said, "You are using the last piece of firewood behind the stove when you ought to be saving it for a real emergency.

"You all damn the federal government and New York City for fiscal irresponsibility, but you are falling right in line with them."

Williams said in an interview that he fears the Appropriations plan does not provide an adequate reserve in the budget. He said he favored extension of the current state sales tax to retail and professional services, a levy that would produce an estimated $60 million.

In addition to the tax collection speedup, the Appropriations plan calls for general fund budget cuts of $26.5 million and a $35 million loan from the highway construction and maintenance fund, financed by gasoline taxes, to the general fund.

The Committee proposed reducing all state agency budgets by 1 per cent for a saving of $11.8 million. It proposed taking an additional $7.2 million out of the corrections system's operating and capital budgets and another $3.3 million out of college spending. The balance is made up of smaller cuts spread among various agencies.