The degree of success that Marion Barry will achieve with the 96th Congress when he becomes mayor may hinge upon what his administration does about a commuter tax.

Area members of Congress, White House aides and Congressional staffers all agreed in interviews that if Barry concentrates on solving such pressing problems as financing the Metro rail system, determing the allocation of sewer capacities throughout the region and other important, but less controversial issues, his new District of Columbia government will get a warm welcome on Capitol Hill.

But if Barry joins with Rep. Ronald V. Dellums (D-Calif.), who will becaome chairman of the House Distric Committee next month, in pressing for a reciprocal income tax for the Washington metropolitan area, those same officials say there will be strained relations between the city and federal governments.

Rep. Gladys N. Spellman (D-Md.) sees a renewed effort to enact a commuter tax as "a threat ot the unique mutual cooperation" the city and its suburban representatives in Congress have enjoyed the last four years.

"It doesn't make sense to push it, because I can't conceive of it passing," said Rep. Herbert E. Harris II (D-Va).

Rep. Joseph L. Fisher (D-Va.) said he may try to talk to Barry, who takes office as mayor Jan. 2, "about the famous commuter tax" in hopes of convincing the new mayor that there are alternative methods of solving the District of Columbia's financial problems.

"I'm eager to assuage the problems," Fisher said, "but to advocate a reciprocal income tax is to bat your head into a stone wall. It may get you plaudits at home, but it won't solve anything because you won't get it."

Getting along with Congress is important to any city administration because the federal government retains considerable control over District of Columbia affairs, even though it has been granting more and more home rule to the city since 1971. Part of the trade-off for granting home rule in the first place was a statute that bars the local government from enacting any form of a commuter tax.

That prohibition has not stopped the city and its allies on the Hill from trying each year to remove the restriction. Walter E. Washington trekked to the Hill annually to testify in behalf of various bills that would allow the city to tap into the income earned by suburbanites who work in the District of Columbia.

The new concern being voiced by opponents of a commuter tax arises from the belief that the combination of Mayor Barry and Chairman Delums will pose a more vigorous challenge than their predecessors, Washington and convicted Rep. Charles C. Diggs Jr. (D-Mich.)

Spellman, who represents Prince George's County, said she and suburban Virginians Harris and Fisher, along with D.C. Del. Walter E. Fauntroy, "are used to working together for the general good. We all served on the COG (Council of Governments) and Metro boards."

She said that cooperation "is in marked contrast to the professional anti-D.C. attitude" expressed by some of their predecessors, most notably former Congressmen Joel Broyhill (R-Va.) and Lawrence Hogan, the new Prince George's county executive who once held Spellman's seat.

Dellums has been an outspoken advocate of removing the barrier so that City Council can enact a commuter tax, or any kind of tax it chooses.

Dellums has been an outspoken advocate of removing the barrier so that Ciy Council can enact a commuter tax, or any kind of tax it chooses.

If Barry-who said during the mayoral campaign that he would "push and work" to have the restriction that bars a nonresident income tax removed-decides to give priority to a commuter tax he will not be without supporters on the Hill.

Fauntroy, who supported Council Chariman Sterling Tucker in the mayoral race against Barry, said he has not yet discussed a legislative program with Barry. But as the city's chief spokesman in Congress, Fauntroy pledged to be "receptive to what the new mayor and council want," including a commuter tax.

Fauntroy's primary goal in the near future is ratification by 35 more state legislatures of the proposed D.C. voting representation amendment to the Constitution. He said he had "made no judgment" on whether seeking a commuter tax could threaten that process, although some members of the Maryland and Virginia general assemblies have suggested that it could.

Rep. Stewart B. McKinney (R-Conn.), the ranking minority member of the House District Committee, expects Barry to use the commuter tax question "as a club, keeping it in his back pocket to see that city gets more equal treatment" in its dealings with the suburbs.

McKinney, who in the past has sponsored legislation to give the city a commuter tax said he plans to support Dellums' approach to the commuter tax issue, which would be to remove the stautory barrier to enactment, rather than his own plan, which would have Congress impose the tax.

An avid defender of central city life, even though he represents a largely suburban district, McKinney joked that his annual introduction of commuter tax legislation has helped suburban congressman here win re-election.

"Herb Harris gets more TV time attacking my commuter tax bill than anything he sponsors himself," McKinney said.

When the discussion of the Barry adminstration gets beyond the commuter tax issue, most congressional D.C. watchers agree that financing the completion of the full, 100-mile Metro system is the top local priority before Congress.

"Metro is a positive tool that the whole region can support," said Harris, "and it will act as a tremendous economic stimulator on the District of Columbia. And without setting up jurisdiction."

The federal government and Metro officials reached tentative agreement earlier this month on a plan whereby the federal government would pay two-thirds of the interest and principal on the $1 billion needed to complete the system.

Harris further hopes to get the United States to agree to pay two-thirds of the cost of refining the bonded indebtedness of the system.

Finally, on Harris' wish list, is a proposal to secure federal participation in the long-term operational costs of Metro.

Another regional problem that could cause a city-suburban showdown is sewage treatment.

"We must try to turn sludge into an economic benefit instead of fighting each other," Harris said, "although we've gotten very little push (cooperation) from the District."

Edward Sylvester, staff director of the House District Committe, listed several other major issues facing the committee in 1979.

They include a revised pension bill for city employes replacing the one vetoed this year by President Carter; finding $19.8 million to retire bonds on RFK Stadium; devising a formula for fixing the annual federal payment to the city, and working toward the 1982 deadline established by the White House Task Force on the District of Columbia for getting the federal government out of the city's budgeting process.

Farther down the list are task force recommendations that Congress and the city establish an appointing authority for local judgeships, and refining the jurisdictional differences between the offices of the U.S. Attorney and the city corporation counsel.

Jim Dyke, a member of Vice President Mondale's staff who is assigned to the task force, said the Barry administration is "off to a good start" with the federal government.

He said aides to Barry have met informally with White House staffers, who suggested the names of some federal workers and others in the private sector who might be hired by Barry.

Dyke said he told the Barry aides that the Carter administration "remains committed to increasing local control" of the District of Columbia government and "looks forward to the day when Washington can be treated like any other major city, rather than something special and different."

Dyke also reiterated the president's opposition to a commuter tax, first voiced by candidate Carter in 1976. But the president's position "is linked to Congress providing sufficient alternative financing," Dyke said.

Many people interviewed on the Hill said they believe that Barry as mayor will be a highly visible and vigorous force in the District of Columbia's dealings with Congress.

"I have the notion that I'll see more of Barry (than of Washington), and I look forward to that," Harris said.

Spellman predicts that Barry "will have a rapport that Walter Washington didn't quite have."

McKinney said Barry "will be a lot more savvy about congressional pitfalls. I just hope Congress, in its drive to cut the budget, doesn't descend more unevenly, on Washington than any other city."

McKinney, who has known the mayor-elect since his days on the school board, said Barry "represents a second generation of city officials. Walter Washington was quiet, steady, but not too innovative. Now we will hear from the city of Washington."

McKinney said Barry "will have an image problem with some members who remember him back when," a refuerence a Barry's anti-establishment activities as a street activist. "But he had every right to be there then," McKinney said.

Barry has acted to smoothe relations with Sen. Patrick J. Leahy (D-Vt.), who will return next year as chairman of the Senate D.C. Appropriations Subcommittee.

Barry and Leahy had a long, private talk shortly after the September primary, according to an aide to the senator. They presumably worked out any hard feelings that remained from Barry's earlier characterization of Leahy as a "rinky dink" senator from fa small state.

Aides to Leahy and Barry also have had lunch since the election.

The Barry aides "understand how the system works, and know where the levers are," said Mike Hall, Leahy's staffer on the appropriations committee. "Bothe (Leahy and Barry) want to avoid public fights, preferring quiet negotiations."

"There should be a little tension-creative tension-in the air, or we're not doing our jobs," Hall said. He said Leahy will employ "the same standards to the Barry administration as he did with Walter Washington, not more lenient or more strict."

Spellman also has high hopes, saying, "I've been watching the evolution of Marion Barry, and noticed that he has managed to retain his old friends and build a new cadre of many unlikely supporters. He'll bring those skills to because the job is enormous."

But in every talk with congressional figures about the city, the conversation eventually comes back to the specter of the commuter tax.

"I hope he'll be more interested in political issues," Harris said.

"A commuter tax showdown can only destroy our relationship," Spellman said.