During the past two months, officials of the National Symphony Orchestra have been eploring three kinds of financial deals to save them from what they predict will be a million-dollar deficit in the coming season.

"We're fighting for our life," NSO president Martin Feinstein said yesterday.

The most delicate of the negotiations involves an attempt to get the Smithsonian Institution to provide enough funding to bail out the symphony. "I am sympathetic," Smithsonian Secretary S. Dillion Ripley said yesterday, "but I don't know where we'd get the money."

A second possibility is a loan from the National endowment for the Arts. At present, the NEA does not have the authority to grant loans. But the House reauthorization bill for the NEA provides for such a loan authority. The bill has yet to be voted on by the full House.

A third project involves applying for a "creative projects" grant from the NEA's music program.

The idea for the Smithsonian bailout began several weeks ago when Feinstein went to see Rep. Sidney R. Yates (D-Ill.), the chairman of the House Appropriations subcommittee on the Interior and related agencies (which include both the arts and the humanities endowments). Yates is a longtime friend and supporter of the symphoney as well as other arts.

The NSO officials "told me about their impending $1-million deficit," said Yates. "They didn't know quite what to do. I said there was only one way to work it out."

Yates suggested drawing on the Smithsonian. the Kennedy Center -- where the symphony performs most of its concerts -- is a bureau of the Smithsonian, as stipulated under the government act creating the center, Kennedy Center officials say that their relationship with the Smithsonian is limited to sending the Smithsonian their standard annual report each year. But Yates said that the Kennedy Center could ask the Smithsonian for money on behalf of its resident orchestra company. (The NSO receives no income from the Center, and pays some $300,000 worth of charges yearly -- much less than what it really owes in overhead, according to Roger Stevens, head of the Kennedy Center.)

"On the basis of my interpretation of the law, the Kennedy Center, as part of the Smithsonian, could receive funds to support the NSO," said Yates. "But they would need three approvals: approval of the Senate, approval of the Kennedy Center board of trustees, and approval of the Smithsonian. I told them, 'If you can do that, you've got a fighting chance.'"

Stevens said, "All I know is that the symphoney called me two months ago and asked if I minded if they went to the Smithsonian." Stevens said that he had no objection: "I said we just wanted the symphony to be healthy."

Stevens also said that the NSO's appeal to the Smithsonian would not involve the Kennedy Center or the board of trustees directly -- "not at this moment," said Stevens.

So Feinstein, along with former symphony board president David Lloyd Kreeger, current board president Austin Kiplinger and soon-to-be board president Leonard Silverstein, went to talk to S. Dillon Ripley.

Feinstein said yesterday that "conversations are taking place with the Smithsonian about the relationship between the Smithsonian and the orchestra." He said that Ripley "was very sympathetic to our plight."

But Ripley, reached yesterday in Connecticut, was less than optimistic: "There have been very few conversations, I'll tell you that," he said. "I wouldn't say the Smithsonian has any funds. We can't make grants out of the blue."

No one is suggesting that the National Symphony become a part of the Smithsonian. In fact, the symphony has no "implicit authority" to go to the Smithsonian, according to Ripley. "The Smithsonian is known to be a friend of the arts," he said. "When I wasn't so busy, I used to be an ardent subscriber and member of the symphony."

Feinstein said that "conversations are still taking place," but when Ripley was asked yesterday if he planned to talk more to the symphony, he said, "No."

In the past, the Smithsonian has met with criticism over some of its numerous projects and financial holdings. In 1977, the institution was the subject of a Government Accounting Office review of its management policies. Other projects have earned public praise: In August of 1979, after three years of discussion about a merger, the Museum of African Art became a part of the Smithsonian.

Feinstein said that the NSO's predicted deficit will include payments for contractual obligations to musicians, soloists, conductors, advertisers and other expenses. But exactly how much will really go unpaid "depends on what kind of contract we have," said Feinstein. "Step by step, we'll face this."

"Everybody we've turned to has given the symphony support," said Feinstein. But not enough. In addition to looking for loans and the like, the symphony is also fund-raising extensively and reshaping its fall 1981 season to include Sunday programs and less repetition of concerts.

"Every orchestra faces a deficit," he said. "And we're number two in fund-raising for orchestras in the country. Why does the Metropolitan Opera have a $14-million deficit? It's the nature of the business for orchestras, for operas, for ballets."

Roger Stevens said, "I don't think they could finish the season if they don't get some help."