He added that City Opera will cancel its entire 2014-15 season if it cannot raise an additional $13 million by the end of December.
Mr. Steel said that while the company had been able to scale back expenses, renegotiate its union contracts and balance its budget in recent seasons, it doesn’t have the money on hand to pay for coming productions.
“We lack a few critical things, and have for a number of years,” he said. “We don’t have much return from our endowment, we don’t have any operating capital, and we don’t have any credit. So what money we have at the beginning of the month is the amount of money we can spend.”
Charles R. Wall, the opera company’s chairman, said that the $20 million goal was “more than we’ve ever raised, as far as I know,” but that he was hopeful that with hard work and the support of a few major patrons, it could be met. He said it would have to be.
“You can’t run the opera on a hope and a prayer,” he said in an interview. “You’ve got to pay bills. And you’ve got to raise the money to pay them. That’s the simplest way I can put it. And you cannot spend what you do not have.”
City Opera had planned to spend $10.5 million on the current season, but so far has gotten commitments for only a little more than $3 million.
Mr. Steel shared the news Sunday with the orchestra, which opposed the move from Lincoln Center and which has seen its pay cut significantly. The players were once guaranteed a weekly salary for 29 weeks but are now paid by the performance and the rehearsal.
Gail Kruvand, the chairwoman of the orchestra committee, said that the move from Lincoln Center had alienated patrons and audience members alike and noted that the company was presenting fewer performances than at any time in its history. She said that the orchestra committee was calling for the resignation of Mr. Steel and for the board to begin searching for a successor.
Mr. Wall said: “George has, and always has had, the complete support of the board, as he should have. He’s done a heroic job.”
The 21st century has been cruel to the finances of City Opera, which Mayor Fiorello La Guardia called “the people’s opera” when it was founded in 1943.
The company began running mounting deficits in 2003. After flirting with leaving Lincoln Center for artistic reasons, it decided to stay when its longtime home, the New York State Theater, was given a major renovation and renamed for its benefactor, David H. Koch.
But going dark for the 2008-9 season while the theater was being rebuilt proved costly. The company lost a year’s worth of ticket sales just as its deficits were growing unmanageable.
That season, the troupe raided its endowment, withdrawing $24 million to pay off loans and cover expenses. The move, coming just when the endowment was already depleted by investment losses brought on by the financial crisis, had long-term repercussions: While the endowment once provided the company with more than $3 million a year in investment income, it now produces less than $200,000 a year.
Last year, City Opera made more from its Thrift Shop on East 23rd Street in Manhattan than from its endowment. The company promised to repay the endowment in stages but has yet to make any repayments, Mr. Steel said.
At that same time, the troupe experienced a damaging leadership crisis. It had hired Gerard Mortier, the iconoclastic impresario who was then the director of the Paris Opera, as its new general manager and artistic director in 2007. But Mr. Mortier ended up resigning before he even officially assumed the post when he found out that his operating budget would be only a little more than half of what he had been led to expect.
When Mr. Steel took over in 2009, City Opera’s finances were reeling. In 2011, he announced that the company could no longer afford to stay in the newly renovated Koch Theater, which included improved acoustics the troupe had long sought.
While the company raised $17 million in the fiscal year ending in June 2011 — a record — contributions fell off again after the company left Lincoln Center and drastically scaled back its productions.
“When you have a smaller aggregate audience, you have fewer people attending the company and fewer potential asks,” Mr. Steel said of the fund-raising difficulties.
Now, in a move that harks back to the company’s populist roots and underscores the start-up mentality City Opera has tried to tap as it works to reinvent itself, the company will seek to raise $1 million of the $7 million it needs to raise by the end of the month through an online Kickstarter campaign.
Mr. Steel voiced optimism that the troupe was poised to survive.
“We’ve been spending a lot of time trying to get the company in good shape, and we have a lean business model, we’ve managed to right-size the organization, we have two years of balanced budgets, we have a much more streamlined administration, we have much better union contracts, and we’re making fantastic art,” he said. “But what we cannot do without is a significant infusion of capital.”