The New York City Opera, which made it through this year's season only with the emergency financial aid of an anonymous benefactor, faces an uncertain future even as it is asking President Reagan to declare it America's national opera company.

The NYCO is carrying an unpublicized $3 million deficit in addition to its estimated annual loss of $7 million. Its summer is uncertain because of the fire that destroyed Wolf Trap's Filene Center and over the summer NYCO faces tough labor negotiations with its orchestra and other unions. Some observers have suggested that the opera's financial problems are so acute that, if it is unable to remedy them, it should shut down.

"Every opera company has its problems," said former diva andd now general director Beverly Sills, ". . . and I'm having mine now. I'm the first one to admit it."

While taking note of poor audience and critical reaction--some of her singers and conductors have booed on stage several times--Sills is nevertheless hopeful about the future. The critics, she said, have told her privately that the quality of the presentations is not the real problem. "They felt," she explained, "the company was going through an identity crisis and that I was going to have to in future years establish just what was the raison d'etre for this company to exist 20 yards across the plaza from the Metropolitan Opera."

Sills pointed out that as general director she lacks something that the NYCO had in the past: "a superstar named Beverly Sills for 14 years on every single damn subscription. It's very easy to run an opera house when you've got that behind you. If you'd like to give me another Beverly Sills--I don't care if it's wearing pants and has a beard--I'll take it."

Board chairman Robert W. Wilson suggested that the company has been the victim of the press, which, he said, "has become so sweepingly negative that I make allowances for it."

Wilson said the quality of the opera "has improved since Beverly Sills took over." He said that "every opera company messes up at least half of the time. I'm not going to let the future of this company be determined by five or six newwmen who carp about it."

As for turning the New York City Opera into the American National Opera, Sills said, "It's not the name, it's the recognition I want-that this is the only American staffed repertory company in the country. We give over 200 performances a year andd at the moment we're about 98 percent American personel.

"If I could get recognition as the national opera company of this country, it would broaden my base of touring. Therefore it would enable more people to hear our young artists.

"It would broaden my base of fund-raising because it's very difficult to raise funds for a company that is indigenous to one area whereas a national company. . .the whole country could take pride in it."

Meanwhile, pleading poverty, the NYCO has asked its lower-paid performers for a moratorium on wage increases and requested that its soloists and principal singers and conductors forgo wage increases of from 8 to 20 percent.

The company is also continuing its 20 percent reduction in the price of subscription tickets--a policy brought about by a substantial drop in NYCO subscriber renewal rate last year. So far, the price cut has brought in about 8 percent more bodies--but less cash--this season.

On the labor front, NYCO's orchestra has engaged as its counsel the same law firm--Sipser, Weinstock, Harper & Dorn--that helped the orchestra at the Metropolitan Opera crush management after a 3 1/2-month shutdown and secure a historic four-performance workweek in 1980. It is the same law firm that helped the dancers of the American Ballet Theatre secure a 40-percent wage increase in their laast negotiations. But there are also indications that the orchestra, aware of the company's financial plight, may be willing to make concessions rather than see it close down.

In Januayr, Mrs. Morton Baum, the widow of the NYCO's co-founder, resigned from its board of directors after a dispute and two more board members, who asked not to be named, said they were considering tendering their resignations because of disagreement with the company's plans.

The New York Times haas taken the opera to task for the quality of its singing, orchestra playing and conducting, staging and productions on several occasions this season. Other publications critical of the opera have been New York magazine and Opera News.

Said Sills, "I think it's fair criticism...I don't see that anyone's gunning for the company. The critics are paid to do their job. They call 'em as they see 'em. That can't alter my own feelings...

"What I'm trying to do is pull away from the iidea of lavish, lavish productsion and try to concentrate on other values. We will try to have one or two lavish productsion but I really think the company ought to turn into much more of an experimental theater--which will bring on many more boos."

Her idea of experimental, she said, includes "less scenery, perhaps moving the time period of the opera, bringing in directors who are not so wedded to the traditional concept of the traditional works, that kind of thing."

As for rumors of internal turmoil at the NYCO, Sills said, "I have total support of the board. I don't feel any turmoil...That's a lot of crap...

"I have no ego trip with this job," she said. "I don't need the money. Her salary is $60,000 a year. And it's costing me money to keep this job at this moment.

"And I don't need the prestige. I'm already a very famous woman...so I take this job and I take everything that comes with it, including the innuendos and the jealousies of certain ladies who can't handle me. I take all that because I love this company.

"My only care is not that I make it into something special--it is something special--my care is that it will remain special forever, regardless of who sits in this office.

"If I'm making wrong artistic decisions, I'll get hell. I'm a very clever woman. I'm not in such an ego vacuum that if I see things are not going the way they should I won't realize it .

"To show how great I am is not why I took this job, I did that already. My niche in operatic hiistory is made. Now I want this company to be secure and to go on forever. If some of my artistic judgments are not good, I'll fixt it up. It's not such a big deal. I'll get it corrected.

Stephen Belth, executive director of Arts and Science Development Service, and an expert in the marketing of the performing and visual arts, suggested that marketing is the key ingredient missing at the NYCO.

"They have to go back to the drawing boards and begin to do the reseach. It is clear that NYCO's audience is not being identifited properly.

"I don't think that prayer is going to help, I don't think waiting is going to help," Belth added. "Something's got to be done. To keep on going would be suicidal. Sitting and waiting and hoping that maybe next sseason will get better will result in more bad money spent on top of bad money.

Sir Rudolf Bing, the now-retired general manager of Metropolitan Opera, said he had attended NYCO performances infrequently but that based on that and what he has read and heard, the company "has a very difficult situation. Miss Sills has so far not shown any success in her job." He offered this advice: "If you begin to lose your audience and you have no subsidy, you'd better give up."

Asked about the insistent rumors that the NYCo is strongly considering shutting down for a year rather than granting raises to its union personnel, Sills responded, "You know, I've heard that, too, but I haven't heard anybody who can explain to me the convenience.

"What do I do with my debt? While you're in business, people are willing to wait, take smaller forms of payment. And my singers, do you think they're going to sit here and wait? My feeling is closing is a disaster. It's not practical."