A design concept sketch of the Bloomburg Bubble at the Hirshhorn Museum and Sculpture Garden. (Diller Scofidio + Renfro)

The Hirshhorn Museum’s Seasonal Inflatable Structure known as the “Bubble” never got off the ground, but many who spent years debating the project say it took up all the oxygen in the room.

The 150-foot-tall project, estimated to cost $12.5 million to $15.5 million, was announced with great expectations in 2009 by new director Richard Koshalek. Promising to rise from the center of the museum and transform the Mall culturally and architecturally, it was killed by Smithsonian officials in June after years of delays and cost overruns. Although officials said half the construction money had been raised, a Smithsonian memo in May estimated that the Bubble would operate at a $2.8 million annual loss, and said that uncertainty about the project had sapped staff morale.

In late May, the Hirshhorn board deadlocked over the Bubble. Koshalek, who had made it his signature project, resigned. Board Chairman Constance Caplan’s resignation last week was the third board resignation since last month, and the seventh since last year.

Over the past decade, the Hirshhorn — the Smithsonian’s only contemporary art museum, and the only contemporary art museum on the Mall — gained a reputation for large-scale, immersive, groundbreaking exhibitions. But Koshalek’s tenure represented a philosophical shift. He brought a sense of showmanship and a brilliance for communicating a larger vision. He sought to connect the Hirshhorn with the global art world, and the world of ideas. “Isolation breeds irrelevance,” he told The Washington Post last fall. The Bubble was to be “called a center of creative dialogue,” Koshalek said, and was to be an international think tank on art and culture, and a way to curate public space.

Instead, debate about the project became a proxy for a larger existential debate about the museum’s core mission and its role in the art world.

In the short term, a search committee and search firm for a new director will be named, as will an acting chairman of the board. But broader-vision issues will take longer. As will the repair work to the depleted board and the museum’s bruised reputation.

“There’s some glass on the floor” Smithsonian Undersecretary Richard Kurin says, but “a lot of people want the Hirshhorn to do well.”

Sponsors, donors and staff members are in a rebuilding mode. “We’ve hit a rough patch, but they say they want it to succeed and move on,” Kurin says. That seems to shake out as a return to the basics.

Says Interim Director Kerry Brougher, “This is a moment where we are going to get really focused on core mission. It’s a mission we’ve had for quite some time: to create exhibitions that address major artistic, cultural and social issues, some of which would seem very relevant for D.C.” Brougher cites the upcoming fall exhibition “Damage Control,” which examines destruction and art and will take up the entire second floor of the museum. “I think we have to get back to taking a look at a museum of contemporary art driven by living artists and the artist themselves.”

Last year, the museum had its highest visitor numbers since 2006, largely the result of blockbuster exhibits, including that of Chinese dissident artist Ai Weiwei. In 2012, 753,000 people visited the museum, up nearly 100,000 over previous years during Koshalek’s tenure. But a month-to-month comparison of visitor statistics for 2013 shows that — without a blockbuster exhibition — attendance is slightly down and is likely to be lower than it was last year.

Brougher acknowledges that fundraising has potentially been hampered by fallout from the Bubble “in the short run.” But “when you have clear focus for the museum and when you know the focus is going right into art, actual programs — and that the public will be gaining the most from fundraising — that helps you fundraise.”

The Smithsonian budget, 70 percent of which is federal money, offers a generous buffer to its museums in uncertain economic times, but Smithsonian leaders oversee many decisions, including fundraising, and have a final say on projects, which in the case of the Bubble was a source of conflict.

In a statement, Tom Hill, who resigned as board chairman in October, stressed what he called the Hirshhorn’s central mission. “It is important for the Hirshhorn to keep the focus on its real value proposition, which is that great art and great exhibitions can spark dialogue, educate, inspire and have real cultural value for the country,” he wrote.

Hill said that when the Bubble debate is forgotten years from now, people “will still be talking about the great experiences they had with exhibitions like Doug Aitken’s ‘Song 1’ projected on the outside of the building, Ai Weiwei’s first American retrospective, the recent Yves Klein retrospective or some other show or artwork that has made them see things differently.”

Board member Dan Sallick says he’s encouraged by the Hirshhorn’s renewed opportunity to focus on art, infrastructure and getting more people excited about the museum. “It’s a chance to engage people from the top board level down to $250 gifts, so there’s a real base,” he says. Every conversation is about how to move forward, he says, and a major component of that will be getting a director who will stay seven to 10 years, and focusing on next year’s 40th anniversary.

In 2008, Sallick says, he was so blown away by a Brougher-curated exhibition called “The Cinema Effect,” an exploration of moving-image art, that he wrote the museum a check the next day. “When you look at the list of shows like that, it makes Ai Weiwei and Aitken seem like part of a continuum,” he says. There is sometimes the suggestion that Koshalek arrived, and suddenly the Hirshhorn did, too. “Richard helped to facilitate” the museum’s blockbuster year, Sallick says, but “we were doing incredibly good things before that, we did good things while he was here and we’re going to do good things in the future.”

Caplan, who took over when Hill resigned and was named board director in May, was an ardent supporter of Koshalek and the Bubble. She emphasizes the importance of the Hirshhorn’s 11,500-item collection, but says she resigned over concerns about where the institution was heading and how it was run. “The real question is what can you do to make a difference in contemporary art that’s about the culture world as well,” Caplan says. “It’s not just exhibitions. It’s really opening people’s eyes to new ways of thinking.”

With regard to funding, donors want to know where their money is going and be part of something transformative, she says.

Koshalek “was terrific, visionary,” Caplan says, and any new director will have to generate the big ideas and work within a Smithsonian hierarchy she characterizes as “lacking inclusiveness.”

Kurin, the undersecretary, says the museum needs a visionary, “but also someone who can manage a complex organization. If you see something at the edge, a new wave of creativity, people rally around that. But the plan must be executable and meet the demands and resources of the Smithsonian.” Among those demands: vagaries of the economy or the congressionally mandated budget cuts known as the sequester.

Tensions between the big ideas and securing funding for them are long-standing and central to the art world. “I often speak about this as redesigning the locomotive while it’s running down the tracks, ”says Timothy Rub, director of the Philadelphia Museum of Art and president of the Association of Art Museum Directors.

The Hirshhorn occupies a special place and “you look for a director who is committed to sustaining a bold schedule of exhibitions and programs,” Rub says. “For someone who can be a very persuasive voice in Washington and nationally about the work of contemporary artists.” At the same time, “any director today, and this is certainly true with the Hirshhorn, has to be talented diplomatically and have both a taste and a gift for constituent management. It comes with the territory.”

Kurin is forward-looking. Plans to transform the south side of the Mall, and include the museum as part of a larger precinct, may be coming by the end of the year, he says. Plans “to really open up the Hirshhorn. We have a garden but it’s hidden. You can’t go from East to West.” Architecturally, there are elements that can achieve the same goals as the Bubble would have, he says. We want “a lightness of being and less bunker mentality.” Such changes might take decades, however, and Kurin wants the new Hirshhorn director to be around for at least half of that time.