One of the biggest, most high-profile deals of the commercial real-estate boom is in danger of imminent default, say people familiar with the matter, signaling the beginning of what is expected to be a wave of commercial-property failures.

The sprawling Manhattan apartment complex known as Peter Cooper Village and Stuyvesant Town -- acquired for $5.4 billion in 2006 by a venture of Tishman Speyer Properties and a unit of BlackRock Inc. -- is running out of cash. As of the end of September, it had $33.7 million left of the...