Michael R. Bloomberg, who was then the mayor, demanded in 2008 that the memorial be completed by the attack’s 10-year anniversary. That meant part of the hub’s roof, which would be the decking under the memorial plaza, had to be built first, adding about $75 million to the budget.

At the same time, the Port Authority was often its own worst enemy.

A 2005 construction contract was supposed to set a guaranteed maximum price, but to accelerate the work, several expensive subcontracts were approved. And in 2008, the authority rejected money-saving suggestions worth over $500 million.

Ultimately, though it may prove to be the building’s saving grace, the architect’s extravagant vision was inextricably linked to the problems.

Mr. Calatrava — known for lyrically expressive structures that are challenging and costly to build — insisted on column-free interiors, labor-intensive building methods and sculptural and curvilinear steel elements that could only practicably be manufactured abroad.

One factory in northern Italy produced one-third of the 36,500 tons of steel in the hub. The steel bill for the entire project was $474 million.

Mr. Calatrava’s boldest gesture called for a roof that could open to the sky. In 2005, not yet convinced that the roof was practical to build, authority officials including David Steiner, a board member, visited the Milwaukee Art Museum to see Mr. Calatrava’s operable roof there.

As they waited outside the museum, the officials were joined by schoolchildren who had also come to watch. When the screen opened, the children applauded. Mr. Steiner turned to Mr. Calatrava and, according to the recollection of those who were there, said: “O.K., Santiago. You can have your goddamn wings.”

It would take another three years to kill this exorbitant idea.

An Irresistible Opportunity

In 2002, the federal government set aside $4.55 billion for Lower Manhattan transportation projects, an irresistible pot of money to local officials who could build something grand without dipping deeply into their own treasuries or spending too much political capital.

Planners envisioned an east-west underground pedestrian network radiating from two new aboveground landmarks: the Fulton Center, which opened in November and was built by the Metropolitan Transportation Authority, and the trade center hub.

“The hub is a project driven by institutional ambition, and once begun, the decisions that have made it so costly became irreversible,” said Lynne Sagalyn, the director of the Paul Milstein Center for Real Estate at the Columbia Business School, who is completing a book on the trade center redevelopment.

In 2003, the authority chose the Downtown Design Partnership, a joint venture, to design the hub’s aboveground entrance and other elements, while an in-house team was to focus on the PATH mezzanine and platforms. The partnership chose Mr. Calatrava as a subcontractor.

Then 52, Mr. Calatrava, a Spanish native, was at the top of his game. His train stations, bridges and cultural buildings were aesthetic sensations, though some have since been criticized for their cost and design.

His spectacular plans for the hub, unveiled in 2004, departed radically from the modest, utilitarian temporary PATH station that had been completed two months earlier for $323 million.