The musicians of the financially troubled New York City Opera went on strike today, one day before the company was scheduled to begin its new summer-autumn season at Lincoln Center.

"I personally am assuming there will not be an opening Thursday night," the opera's chief negotiator, Martin J. Oppenheimer, said today.

The two sides were scheduled to meet at 10 a.m. Thursday with a state mediator, in what an opera spokesman tonight characterized as a "last-ditch effort."

The musicians said they would set up a picket line at Lincoln Center Thursday, and the company said it would make no attempt to break the strike. While officials refused to discuss specifics of the company's financial picture, a spokesman for director Beverly Sills said a strike would not put the company permanently out of business.

The 69-member orchestra has been without a contract for 10 months, and little progress has been made in negotiations for a new agreement. Last autumn's season was presented under a temporary extension of the expired contract.

The dispute centers primarily on the number of weeks the musicians will work. Other key issues include the number of performances per week and pay increases at a company with financial problems.

"They're asking for a package that would increase our costs 50 percent this season and over 150 percent over the next three years," Oppenheimer said.

During the 1981-82 season, the orchestra had 35 weeks of work, vacation and supplementary unemployment benefits, compared with 20 weeks the City Opera is offering for the upcoming season. The union is asking for 25 weeks.

The musicians also are asking for a five-performance work week instead of the six performances stipulated in the old contract. Such a reduction in workload would require substantial overtime payments to the players or the hiring of additional musicians for City Opera's orchestra.

Musicians at the Metropolitan Opera and at the New York Philharmonic have a four-performance work week.

Under City Opera's old contract, musicians earned $535 for a six-performance work week, compared with $735 for a four-performance week at the Met. City Opera had offered a 6.5 percent increase under a one-year contract, while the musicians have asked for between 10 and 15 percent over three years.

Music industry executives who asked not to be named said the labor dispute is expected to set the tone for musician-management negotiations in the classical performing arts in New York--and perhaps across America--for the remainder of this decade.

If City Opera succeeds in overcoming the musicians' objections, these sources said, other performing arts organizations soon will seek similar concessions.

City Opera's attendance has fallen sharply in the past three years, and the company has canceled its annual spring season. In an attempt to find a new audience, it has turned its annual September-November season into a July-November run.

But City Opera also has fallen on hard times in other areas. Last year, because of the fire at Wolf Trap Farm Park, it did not perform in the Washington area at all, nor will it this year. And the company's annual month-long visit to the Los Angeles Music Center also has been terminated.

The musicians argue that City Opera's financial and artistic difficulties are not their headaches. But City Opera's Oppenheimer claims the opposite is the case: "Our problems are their problems . . . I understand their problems and we're sympathetic. The answer is to build a sound financial base for the company. We're proposing a contract that keeps the body alive" while seeking more funding and performances.

"When a manufacturing company loses orders, it lays off people. They want us to pay for the weeks of work they had in the past. We can't. It flies literally in the face of reality to pay them for weeks of work that are no longer available. They have shut their eyes to the reality."

Until this year, many of the musicians subsisted primarily on their City Opera incomes, supplementing this with temporary jobs and summer work at festivals. The lengthened summer season at City Opera precludes supplementary work. All of these factors, plus a resentment over not being consulted about the company's plans, have contributed to a mood of bitterness among the musicians.

Sills today declined comment on any aspect of City Opera's situation.