The fate of the “Bubble,” the seasonal inflatable structure that was supposed to rise from the top of the Hirshhorn Museum and Sculpture Garden to create a culturally and architecturally transformative space, is up in the air.

The 145-foot-tall structure that was to house performances and cultural dialogues has been a signature project of museum director Richard Koshalek, who arrived at the Hirshhorn in 2009 and announced the project to great fanfare the same year. But the timetable has been pushed back for a second time, and construction costs, originally estimated at $5 million, have escalated to around $15.5 million, said Smithsonian officials. They now say the Bubble will not go up until 2014, if it does at all.

“I truly understand the complexity of all this,” Koshalek said in an interview with The Washington Post. He calls the project essential to the future of the Hirshhorn. “I also know that in the world of proposing ideas like this, there are unbuilt projects. We could get to that point where this could get unbuilt.”

Koshalek came to the Hirshhorn from the Art Center College of Design in Pasadena, Calif., where he pioneered a number of programs, including Art Center for Kids and Art Center at Night for adults. But a planned expansion to the center by architect Frank Gehry sparked enormous debate, was not built and led to Koshalek’s ouster.

The Bubble has also become controversial. Since 2010, when Bloomberg LP donated more than $1 million and the project was tentatively renamed “the Bloomberg Balloon,” there have been no other funding announcements, and last summer, the date for it to take form was moved from this year to 2013. Last month, Hirshhorn board Chairman J. Tomilson Hill resigned without citing a reason. From the beginning, critics (including Blake Gopnik in The Post) worried the Bubble would take time and resources away from the Hirshhorn’s core focus on contemporary art.

Still, Richard Kurin, the Smithsonian’s undersecretary for history, art and culture, said half of the construction costs have been raised. But the project will not move forward if the money isn’t there, he said. If you want to buy a house, “you’ve got the money or not. Simple.”

“From my Smithsonian experience, the Bubble would be very popular and generate enough to take care of operational costs for the year,” he said. There is great enthusiasm for the idea architecturally and in terms of curating public space, he added.

“We hope to make a decision by spring 2013 that would enable us to put up the structure in 2014.”

In a statement released Thursday, Hill said: “In a difficult economy, museums must never put their core mission in harm’s way by overextending financially. If the Hirshhorn moves forward with the Seasonal Inflatable Structure project, my hope is that it will be done with the utmost transparency, accountability and emphasis on sustainability.”

Hirshhorn attendance numbers are up more by than 100,000 over this time last year. This year, the Hirshhorn has had enormous programming successes: Chinese dissident artist Ai Weiwei, Barbara Kruger and the spring’s “Song I” by Doug Aitken, a multimedia piece projected onto the side of the Hirshhorn building. Museum officials say that kind of programming must continue.

Tensions around creation are inherent in art, Koshalek said. “In a way, you have to embrace controversy. There’s no way you can avoid it. No way you should avoid it.” He sees the churn around the Bubble project as a metaphor for what’s going to happen when the structure goes up. “I know there will be people who say, ‘I don’t want this institution to change,’ ” and a discussion about their concerns is essential.

“If you have an idea that’s of the moment, that’s important, the money can be found,” he said.

Kurin acknowledged the challenges. “Nobody has done this before, nobody has built this kind of thing,” he said. If everyone whom they are targeting for funding comes through, the project will proceed, he said.

Meanwhile, the board is divided among those who want the project to move forward, those with doubts and those who think Hill’s resignation should call a stop to the proceedings, at least for now.

It’s the tension of creation. “Everyone wants to do the right thing,” said one source who spoke on the condition of anonymity because discussions about the project are ongoing. It’s just that “nobody has figured out what is the right thing for the Hirshhorn and the Smithsonian.”