At his April inauguration as Chicago's first black mayor, Harold Washington confidently proclaimed that he would break the power of the old-line Democratic machine and usher in a reform era that would serve as a model for the nation.

But less than three months later, a series of bruising, losing encounters in the City Council and the Illinois Legislature has left Washington struggling to find momentum and direction for his fledgling administration.

Although there have been some victories, an air of ponderous deliberation has settled over the paneled offices in City Hall, where Chicago's chief executives for more than 50 years have customarily ruled rather than presided.

Even some of Washington's staunchest supporters are privately fretting that the new mayor's ways so far seem unsuited to answering the urgent needs of a cash-poor city and of the underprivileged minorities who form the core of his support. They are wondering whether he can transfer his sweeping podium style to the mundane but critical back-room wheeling and dealing that made Richard J. Daley such a legend and gave Chicago its reputation as "the city that works."

There are wider implications attached to Washington's performance. His election triumph over Republican Bernard Epton, who got a strong white backlash vote, vaulted the 61-year-old former congressman to the front ranks of the nation's urban black politicians. With black leaders intent on expanding their impact on 1984 Democratic presidential politics, Washington's effectiveness in this key Democratic city takes on special significance.

But a snail-like pace of new appointments, the continued impasse between Washington and an opposing majority of white aldermen, and unexpected city defeats at a recent state legislative session in Springfield have slowed whatever momentum the mayor once had hoped for.

And looming on the horizon are wage talks with transit workers, police and firefighters, whose contracts begin expiring in a few months. These promise only headaches for Washington, who already faces a $45 million deficit this year.

At Springfield, the city's usually dominant and cohesive block of Democratic lawmakers was jarred by squabbles between the mayor and his legislative leaders over how to pry new revenues out of Republican Gov. James R. Thompson and unsympathetic downstate legislators.

As a result, Chicago fared badly in getting a chunk of new state tax revenues, and a transit aid package got derailed. The Chicago Transit Authority (CTA) and its regional partner may need up to $150 million to keep the trains and buses running, a vital concern of low-wage workers. Washington and Illinois House Speaker Michael J. Madigan continue sparring over this major issue without resolution.

A major clash on the city's deficit is brewing this week. Washington has requested television time Monday night to propose his solution, which likely will include some layoffs of city workers and possibly new or revived taxes.

But the powerful new chairman of the city finance committee, Alderman Edward M. Burke, says he will fight any tax boost "as long as I am chairman," a vow with a special twist for Washington. Burke is one of 29 white aldermen who seized control of the 50-member, all-Democratic City Council on the mayor's first day in office.

They ousted the mayor's men from every important committee chair and have become entrenched, resourceful opponents despite assurances of cooperation from their leader, Alderman Edward R. Vrdolyak, who also is Cook County Democratic chairman. Vrdolyak may try to upstage the mayor by offering his own financial relief plan.

Major bankers and bond rating analysts are watching these political maneuverings closely to see whether the city, which annually borrows millions of dollars in short-term notes, is as good a risk under Washington as it became under his predecessor, Jane M. Byrne. She discovered that the mayor she succeeded, Michael Bilandic, had left huge hidden deficits, and now she has done the same thing to Washington.

Most of Washington's troubles can be traced to the May 2 Vrdolyak coup. For despite such reform moves as opening more government proceedings to the public, Washington lost a series of court challenges to Vrdolyak and ever since has found himself in protracted behind-the-scenes negotiations with tough ward leaders who fear that continued reform will cut their power over jobs and other traditional pork-barrel matters.

Conscious of his unique status as a black in the city's highest office and the fact that he does not control the council, Washington tries to use the symbols of his position to increase his impact on what has become an unruly and unpredictable situation.

There are pluses and minuses to this strategy. He prefers to speak from his own offices, where the setting is solemn and authoritative. But he seldom has the kind of impromptu session with the media in corridors, elevators and back rooms that can lend a sense of excitement and movement to a politician.

Recently, for example, after a relatively peaceful council meeting, Vrdolyak held forth before a phalanx of cameras, quipping and discussing a possible new cigarette tax. Meanwhile, Washington was passing through the same back room, smiling and nodding--but saying nothing.