D.C. Mayor Walter E. Washington and his budget director, Comer S. Coppie, acknowledged this week in Senate testimony that their failure to budget funds for a Metrorail subsidy is largely a ploy to gain support for a regional transit tax, possibly including city taxation of suburbanities.

Coppie told the Senate District Appropriatins Subcommittee that regional taxation is a long-term goal and declared that "the city will have a responsibility to come up with the necessary money" to pay its immediate share of running the expanded subway system.

The mayor said he wanted to "use the pressure" of withholding funds to gain support for the regional tax.Coppie said one approach would be "to give (the city) authority to tax nonresident income."

Sen. Patrick J. Leahy (D-Vt.), the Subcommittee's new chairman called this "as subtle as a sledgehammer."

Since the city has not proposed either the $850,000 needed in the current fiscal year or an estimated $13 million in the next fiscal year in its alreadly tight budgets, the potential source of subsidy funds remains a mystery.

Unless the money is provided, the region faces the stark prospect that the existing five-mile downtown subway line may have to shut down and the 12-mile second line may not be opened to passengers as scheduled on July 1. The second line will run from the Stadium-Armory station through downtown Washington to National Airport.

Until very recently, Coppie had told a reporter he knew of no plan for the city to come up with the subway money, other than through a regional tax source. The mayor said substantially the same in a recent news conference.

With less than four months to the opening of the second subway line, Metro staff officials have expressed a growing anxiety over the District's course.

Suburban members of the policy-setting Metro board, asked about the issue at Thursday's meeting, gave diplomatic responses clearly calculated not to antagonize their District colleagues. The suburbanites acknowledged concern that voided confidence in a successful outcome.

"My own expectation is that some time soon the District will present a plan (to Metro)," Joseph S. Wholey, first vice chairman of the Metro boatd and chairman of the Arlington County Board, said. "It is the District's responsibility to do so."

Metro board chairman Francis W. White, a Prince George's County Council member, stressed that it is too late - to enact a regional tax this year. He noted that the Virginia legislature had adjourned and the Maryland legislature soon will follow.

In Congress, suburban lawmakers have consistently resisted what is generally called a "commuter tax" - a levy on the wages of suburbanities who work in the city to help aby municipal expenses.

Although Metro is a regional project, its financing including the payment of its operating deficits, is based on contributions from tax revenues by eight cities and counties in the region.

The question posed by the District government maneuver is whether suburbanites, who already pay part of the cost of Metro to their home jurisdictions, would be willing to contribute additionally to help defray the city's heavy cost burden.

An initial attempt, led by D.C. City Council Chairman Sterling Tucker man, was shot down late last year at a meeting of area officials.

The officials agreed to explore the idea of having all jurisdictions levy a specific tax to support Metro, but did not consider the idea of the subrubs sending money into the city to help defray its costs.

In appearing before the Senate committee on the city's supplemental budget on Monday, the mayor and Coppie did not intend to touch upon the Metrorail subsidy issue. Leahy had read about it in the newspapers, and questioned Washington about it. The mayor asked Coppie to respond.

"The city's commitment has to be to get the authority to tax nonresident income in order to do this job, or to move toward some kind of overall regional plan of financing," Coppie told the Subcommittee.

"The city will have a responsibility to come up with the necessary financing," he continued. "But we feel that over the longer term . . . indispensible to the success of Metro is . . . either some form of overall regional plan or broadening the city's tax base to give it the authority to tax nonresident income . . ."

Leahy responded with a question: ". . . Is this as subtle as a sledgehammer, suggesting to the outlying areas that they might want to re-examine their opposition to such things as a commuter tax, and things of that nature?"

I think that is on target, sir," coppie agreed.