The Smithsonian Institution and the National Gallery of Art said yesterday that they would be forced to close their doors for two or three days a week if a government-wide 32 percent budget cut goes into effect at the beginning of October. But there was widespread doubt that the gloomy scenario would ever materialize.

Like other federal agencies, the Smithsonian was required to give the Office of Management and Budget a plan for handling deep cuts that might be triggered by the Gramm-Rudman-Hollings act. The institution also sent notices of possible furloughs to more than 6,600 employees.

But Roger Kennedy, director of the National Museum of American History, said the deep cuts were "extremely unlikely." On the Hill, a Democratic aide said the exercise was simply "the administration trying to play tough."

In a memo sent yesterday to all employees, the Smithsonian's top budget official said a 32 percent budget cut is unlikely to remain in effect for the entire fiscal year but added that "there is a good chance that such a reduction will be in effect for some portion of the first quarter of FY 1991 while the Administration and Congress attempt to work out a deficit-reduction plan."

The Smithsonian memo said the plan submitted to OMB was designed in part to "demonstrate that it is unavoidable that the impact upon the public will be as major as in other programs." The plan anticipates closing its museums -- as well as the National Zoo -- on Mondays, Tuesdays and Wednesdays.

Smithsonian officials said yesterday that the possible closings were not simply a scare tactic to win congressional sympathy. "We certainly are not trying to scare anybody," said Alan Fern, director of the National Portrait Gallery. "They're scaring us."

Smithsonian spokeswoman Madeleine Jacobs said the possible closings would save the expense of two full guard shifts a day at a dozen museums. She declined to say how much money would be saved or how many guards are deployed at those institutions. "You have to pay them and it's expensive," she said. The Smithsonian has not determined how much could be cut from the budget without forcing some museum closings, she said.

If the plan were put into effect, the Smithsonian would have to trim about $89 million from a $279.3 million departure point set by OMB. In fiscal 1990, the institution got $267 million from the federal government; so far, a House subcommittee has approved a $313 million budget for fiscal 1991.

American History's Kennedy said the consequences of any major budget cut at the Smithsonian would be very unpopular with the public. The cuts have "got to get well below 10 percent -- down below 5 percent -- before it's conceivably acceptable to the American people," he said.

About a third of the Smithsonian's staff members are federal employees and the rest are paid through the institution's trust funds. But the institution plans to impose furloughs across the board. The Smithsonian's "trust employees" staff the museum's profitmaking ventures, such as its shops. Since revenues would be curtailed if the museums were closed for part of the week, the trust employees would also be subject to furloughs. Yesterday's notice provides for furloughs of up to 22 days.

At the National Gallery (which is not part of the Smithsonian), spokeswoman Deborah Ziska said that 85 percent of the $53.9 million budget in fiscal 1990 went to personnel costs. (The federal government provides 80 percent of the gallery's total budget.) A 32 percent cut would require the gallery to furlough some of its 999 employees and to close for two days a week. "We're taking it all very seriously, of course, but we're hoping it won't occur," she said.

The National Endowment for the Arts and the National Endowment for the Humanities also submitted plans to OMB yesterday. While the NEA did not respond to inquiries about its plan, NEH said it has already imposed a hiring freeze. If the 32 percent cut went into effect, employees probably would be furloughed two days a week and grantmaking activities would be "severely disrupted," the endowment said.