Design concept sketch of the Bloomburg Bubble at the Hirshhorn Museum and Sculpture Garden by Diller Scofidio + Renfro. (DILLER SCOFIDIO + RENFRO)

The Seasonal Inflatable Structure project, informally known as “the Bubble,” is dead, the Smithsonian Institution and the Hirshhorn Museum and Sculpture Garden announced Wednesday.

The decision by Smithsonian Secretary G. Wayne Clough and Undersecretary Richard Kurin comes ahead of a June 24 board of regents meeting and caps years of high-level debate and division about what the Bubble would mean for the Hirshhorn and the Mall. Hirshhorn Director Richard Koshalek, who announced his decision to resign in late May after the Hirshhorn board split over whether to proceed with the project, will step down June 29, officials said.

“If the board were more together and if we were seeing more results of that, then we might have made a different decision,” Kurin said. “Because it’s divided, it makes it hard to move forward.”

Koshalek called it a larger question of vision and purpose. “My feeling is when you become the leader of an institution, your responsibility is to raise the standards of expectations for that institution,” he said. “When it’s not open and responsive to these ideas, it’s not the appropriate situation for somebody like myself.” The Bubble “should have happened, and it should have happened in Washington,” he said.

Accounts of the May 23 board meeting differ. According to a source close to the Smithsonian Institution, a slim majority of the Hirshhorn board favored proceeding with the project. Another source with knowledge of the meeting said a number of board members were absent, and those who did not leave official word as to their decision were counted as supporters. Kurin declined to go into specifics about the board’s deliberations. In the past two weeks, two board members, including Paul C. Schorr III, the leading advocate of the Bubble, have resigned. Rebuilding the depleted board, which has lost six members since last year, will be a priority of the new director, Smithsonian spokeswoman Linda St. Thomas said.

The Bubble was announced in 2009 as Koshalek’s signature project — a way to make the Hirshhorn central to global conversations about arts and culture ideas and policy. The 150-foot-tall structure — which was to rise from the center of the museum as a space for special events, symposia and exhibitions — initially earned national attention and plaudits, with supporters characterizing it as visionary and transformative. Then construction costs ballooned. There has been only one $1 million announced donation of the estimated $12.5 million cost (although officials say about $7.8 million had been committed), and the project soon became “bubble, bubble, toil and trouble” to critics who said it was drawing resources and focus away from the Hirshhorn’s core mission of displaying contemporary art. At least three Bubble postponements and stalled fundraising efforts followed. Last month, an internal Smithsonian memo said that the Bubble would operate at about a $2.8 million loss and that staff morale had been affected by the ongoing uncertainty surrounding the project. Wednesday’s announcement means the Hirshhorn must return or forgo any money raised or committed.

“There was and has been a lot of support for the idea and concept here,” Kurin said. But “a lot of times ideas meet reality and the reality was the fundraising just was not bringing it in. Here we were four years later. What’s the wisdom of going ahead? The dollars to fabricate weren’t there. We didn’t have a viable model to operate on a yearly basis.”

Kerry Brougher, deputy director and chief curator of the museum, will become acting director, beginning June 30. The “idea now, especially in tougher fiscal times, is to turn our attention toward keeping the Hirshhorn the great museum it is,” said Kurin. “We will search for a new director, and the museum and its staff will go forward.”

Koshalek, 70, who will be traveling to New York and Europe and returning to California in late summer, said he will be working on a new project.

“I will be focused on what we call the ‘Tech Tent,’ a portable global classroom,” he said, that will act as the same kind of arts-and-cultural think tank he intended the Bubble to be, but on a smaller, less expensive scale, untethered to any existing structure. The project would be studied and built on a university campus in Southern California within the next two years, he said, declining to give further specifics. It is not the Bubble, but it would be the “same high level of originality as the Bubble was . . . but be more feasible in terms of design, costruction and installation.”

Koshalek has a history of ambitious, polarizing ideas.

Before coming to the Hirshhorn, he pioneered programs and major expansions at the Art Center College Design in Pasadena, Calif. But a planned expansion by architect Frank Gehry prompted critics to charge he had veered too far from the school’s educational mission. It never got built and led to his resignation. He has characterized controversy and tension as inherent to creativity.

“I see my responsibility to propose bold ideas,” Koshalek said. He recounted recent Hirshhorn successes, such as the 2012 multimedia projection “SONG 1” by Doug Aitken. He said he had nearly a dozen more ideas.

Of his projects, Koshalek said: “If they don’t happen, they just don’t happen. You move on and build somewhere else. I remain totally optimistic.”