Completion of the third tunnel rose to the top of Mr. Bloomberg’s to-do list, his aides said, after a frightening meeting in 2002, during his first weeks as mayor. Officials from dozens of agencies had gathered to talk about preparedness for events like terrorist attacks and natural disasters.

“As ugly and disastrous as those scenarios were, none of them came close to the possible collapse of one of the two water tunnels that would make half the businesses and residences inside the city of New York uninhabitable,” recalled Kevin Sheekey, a former deputy mayor, who was at the session.

At the time, the two existing tunnels were carrying more than a billion gallons of water to the city from a reservoir in Yonkers every day, as they had for much of the last century. They had not been closed or inspected since they went into service, Tunnel No. 1 in 1917 and Tunnel No. 2 in 1936. Engineers had tried to shut the older one temporarily in 1954, but a giant valve beneath Central Park trembled and began to crack, so they stopped. That year, the city authorized construction of a third tunnel, which would allow the older ones to be examined and the operating equipment to be overhauled.

Actual digging did not begin until 1970.

In the decades that followed, lawsuits, financial crises and other priorities sometimes brought the tunnel construction to a halt — “The $1 Billion Tunnel to Nowhere” was the title of a New York magazine article published in 1979 — or to move along so slowly that completion remained beyond the sights of most people alive in 2002.

That left the city vulnerable to the potential collapse of old tunnels hundreds of feet below ground, or, perhaps more likely, the breakdown of equipment which could not be repaired.