She had tried to think of everything to make this year’s gala perfect.

Celebrity attendees were confirmed. Starting bids on auction items were locked in. The floral centerpieces had even been pared back so that diners could talk across them. (That had been a problem last year, when the orchids got in the way.)

“They’re buying a $2,000 or $3,000 ticket — they want to have a good experience,” said Mónica Ramírez-Montagut, the executive director of the Parrish Art Museum, who was overseeing its annual Midsummer Gala. “So it’s really important for us to be able to deliver that.”

The gala at the Parrish, situated amid the tall grasses of Water Mill on the East End of Long Island, is among the signature events in a series of high-end fund-raisers that are a staple of Hamptons summers, with their champagne upon arrival, designer outfits, air kisses and general hobnobbing among billionaires and millionaires who make up some of the nation’s wealthiest elite.

This year, the pressure on nonprofit institutions to raise money at events like these is higher than ever. Federal support for the arts has become unreliable, and tapping just a little bit more of the immense wealth in the Hamptons could make or break an institution.

That means more pressure on directors such as Dr. Ramírez-Montagut, who must work harder than ever to please sometimes finicky benefactors.

“A good gala is increasingly critical and instrumental for museums’ sustainability and financial stability, which is why we go all out,” she said.

At the Parrish gala last Saturday, called “Echoes of the Cosmos,” all did not go as planned. One of the celebrity attendees who was to serve as a big draw, the fashion designer Donna Karan, told organizers she had Covid and couldn’t make it. Jeff Gordon, the former NASCAR driver, canceled at the last minute, too, telling the staff that he had arrived in the Hamptons but had forgotten to bring nice pants.

Dr. Ramírez-Montagut sighed after hearing the bad news a few hours before the event was to begin, and pressed on. There was no time to do much else.

The Parrish typically relies on its summer gala to raise at least $1 million — about a fifth of its budget — from ticket sales, sponsorships and an auction. This year, museum leaders were hoping the auction proceeds would also help cover another $140,000 to pay for art education programs for people with dementia and other special needs, as the federal government seeks to cancel grants.

The unreliability of federal money had already cost Dr. Ramírez-Montagut one of the museum’s longtime educators, who is retiring this summer because of the uncertainty. Dr. Ramírez-Montagut also faced a personal setback when President Trump put on leave the entire staff of the Institute of Museum and Library Services, of which she was a board member, in an apparent attempt to shutter the agency that provides most federal support for libraries and museums.

“The whole running of a museum has always been stressful,” she said. “A good gala can make it or break it. It can mean whether I can hire people or whether I need to lay off people.”

Dr. Ramírez-Montagut, who joined the museum in 2022 and previously had run museums in Michigan and Louisiana, spent months planning this year’s event.

“When I get on that stage and see 450 very important people in the world, I need to make a good impression and have the night run smoothly,” she said. “And it has to be fun.”

She arranged for a dance troupe, Parsons Dance, to perform on the grass during cocktail hour and at other interludes throughout the evening, to keep things moving. She worked with Hedley Studios, which helped sponsor the event, to place drivable, miniature replicas of a Ferrari, an Aston Martin and a Bugatti on the lawn for guests to fawn over. She rented Sputnik-style light fixtures to dangle over diners, similar to the décor in the Metropolitan Opera House. From the signature cocktails to the silver balloons scattered on the dance floor to the noted artists who could mingle with the guests, the whole evening needed to be, she said, “polished and sophisticated.”

“You even need to wear the right thing, and to make sure your delivery is polished,” said Dr. Ramírez-Montagut, who trained as an architect in Mexico, where she grew up, and did postgraduate studies in Spain. “And that can be a deal breaker. These are really high stakes.”

At last year’s gala, a donor had complained about sitting too far from the stage, so this time Dr. Ramírez-Montagut placed a few V.I.P. guests front and center — but also scattered them throughout the space to make sure everyone, regardless of where their table was positioned, would feel important.

Seating was among the most complicated parts of the event planning. The day before the gala, museum staff members gathered in a small conference room over a map of the tables, color-coded with the amounts guests had spent to reserve them. Orange was for high-level donors who had paid $50,000 for 12-person tables; $30,000 tables seating 10 were purple, and so on.

Workers were swapping out small tabs labeled with the names of ticket holders, trying to settle on a satisfactory seating arrangement.

“The whole thing is a little Game of Thrones-y,” said Agatha Emmett, the special events manager at the Parrish.

There were many boldfaced names to satisfy. Greg Lippmann, an executive at an asset management firm and onetime mortgage trader who inspired a character in the movie “The Big Short,” would be seated at a table toward the back but near Dr. Ramírez-Montagut and other big donors and gallerists. A table would serve as a buffer between John Paulson, a billionaire hedge fund manager and major Republican donor, and Dennis Mehiel, a major Democratic donor who made his fortune in corrugated cardboard. The artist Rashid Johnson would sit near the front, next to Larry Milstein, a scion of the billionaire real estate family and a museum board member.

A crisis emerged: Bank of America wanted four additional tickets, but where to seat the extra guests? Dr. Ramírez-Montagut insisted her staff find space for them.

“I mean, they used to be our big funders,” she said. She hoped attending this year’s gala would help the bank re-engage.

On Saturday afternoon, an hour before guests were to arrive for cocktails in the meadow, Dr. Ramírez-Montagut stood at the tables, still futzing with place cards.

She noticed smudges on the elegant but transparent plastic chairs; a dozen event workers, armed with Windex, started wiping them down. Bartenders were ready to serve the Cosmo-Not, a drink with a ginger hibiscus salt rim and orange twist. Valets were in place to point guests toward the barnlike museum’s long hallway, past a trio of musicians, one of whom strummed a harp. Attendees would need to take care not to trip on a wooden foot bridge that Dr. Ramírez-Montagut nicknamed “the channel of death of the stilettos.”

“They know the drill,” she said, shrugging off worries about busted ankles.

Soon, the elite of the Hamptons arrived to stroll through the galleries, mingling among the spaces named for benefactors like them.

“They’ve really upgraded the quality of the show,” said Mark Fehrs Haukohl, an art collector who uses the title “sir” and was wearing a purple double-breasted suit jacket.

After cocktails in the meadow, dancers beckoned the group to sit down under soft blue lighting to enjoy charred New York strip steak with cauliflower soubise and marbled potato fondant, followed by tiramisù topped with caviar-like pearls of espresso and served in fancy tins. An auctioneer from Sotheby’s goaded diners, whose collective wealth could make a dent in world hunger, to raise paper fans to make donations to the museum’s programs for immigrant youth and people with Alzheimer’s.

“There’s a lot of supporting to do these days,” said Barry Holden, an artist and the husband of Nina Yankowitz, another artist.

The event raised $1.4 million. Satisfied that the evening was a success, Dr. Ramírez-Montagut left shortly after 11 p.m., while the dance music still blared and younger guests twerked next to older couples doing the two-step to a remix of the “White Lotus” theme song.

Inside one empty gallery, Carlton Jones, a fashion designer, stole a quiet moment alone with the art. He took a selfie and then stood in the vast space, looking at the blocky blues and blacks of a giant Sean Scully painting.

“What is the word to describe this?” he said, pausing to think. “Jubilee.”