The Reagan administration's proposal to begin phasing out federal operating subsidies to Metro and about 350 other U.S. transit systems next fiscal year has encountered stiff opposition on Capitol Hill.

Many transit specialists predict Congress will pass a one-year extension of the current program of $1 billion a year, although Urban Mass Transportation Administration chief Arthur Teele says such a bill would face a presidential veto.

Despite the White House's opposition, the Senate banking committee has already approved an extension bill that rejects the one-third cut in operating aid in fiscal 1983 the administration wants. In the House, the public works committee has reported out legislation that would go further than that, retaining operating aid for four more years, while placing a ceiling on it.

Both bills are an indication of the unhappiness Congress has shown over the plan to phase out all operating aid by fiscal 1985, a cornerstone of the Reagan administration's transit policy.

Federal subsidies covered about 17 percent of the cost of running transit in this country in 1980, according to the American Public Transit Association (APTA). The association argues that ending the aid would drive some systems into bankruptcy and has led the fight to save it, drawing support from such groups as the National League of Cities and the National Association of Counties.

For Metro, an extension would restore about $11 million in operating aid it had expected to lose in fiscal 1983. "That would help considerably," General Manager Richard S. Page said. The money could lower the $188 million that area governments are scheduled to contribute toward Metro's $337 million operating budget for fiscal '83.

Metro this year will receive about $25 million in federal operating grants, about 8 percent of its total running costs. Smaller systems generally are more dependent than Washington on federal money: the bus system of Flint, Mich., for instance, got 42.5 percent of its revenues from the program in 1980, according to APTA.

The administration argues that capital aid to help buy rail cars, buses and other high-cost equipment is a legitimate federal role, (though due to the recession, levels will be lower than in past years and new construction starts rejected). But once the equipment is delivered, Teele has said, transit systems must be able to run it without federal help.

The administration has maintained that operating aid has encouraged transit managers to grant overly generous wage and benefit packages to unions and to allow productivity to remain low.

Attempting to address some of the objections, transit officials have suggested that federal aid could be reserved for nonpersonnel expenses such as fuel, insurance and maintenance of equipment that federal dollars helped buy.

"We think a maintenance support program is perfectly consistent with the administration's philosophy of not being involved in labor negotiations," said APTA executive vice president Jack Gilstrap. The administration has agreed to allow some spare parts costs to be moved from operating to capital programs, but rejects the other ideas.

The bill approved by the House public works committee would set up a block grant program giving transit systems some flexibility in dividing their share of the money between operating and capital expenses. Spending for operations would be capped at 1982 levels, however, with maintenance to get first priority for the money. A higher match ratio would encourage managers to use grants for capital rather than operating expenses.

The bill's funding level assumes that federal gasoline taxes will be raised by five cents, with one cent of it, or about $1.1 billion per year, to go to transit. Now that President Reagan has come out against such an increase, however, many transit specialists predict that a simple one-year extension is the most likely outcome.

The Senate banking committee, meanwhile, unable to settle differences among members over operating aid and other issues, already has reported out such a bill. Both bills are authorizing measures, meaning that actual spending under either one would be possible only after further votes by Congress.

Many transit officials feel the administration has softened its stance on operating aid in the face of congressional opposition, but UMTA's Teele maintains that is not so. He will recommend a veto of any bill that keeps the aid at current levels, he said, though he said he could not specify what, if any, level less than 100 percent would be acceptable.