When the first phase of construction is finally finished this fall, the enormous Essex Crossing development will begin to transform the Lower East Side of Manhattan: luxury condominiums, a vast underground market with local vendors, a senior center, a museum, a public park, a bowling alley and the first multiplex movie theater in the neighborhood.

But the biggest draw for New Yorkers is the affordable housing.

In the past two months, over 93,000 people have applied for 104 apartments in one of the planned buildings.

“Ninety-three thousand — that’s no joke,” said Yuh-Line Niou, the state assemblywoman for the district, who has been helping local residents apply for the apartment lottery. “It shows the incredible need here.”

Last fall, Ms. Niou won the seat that a fellow Democrat, Sheldon Silver, had vacated after being convicted on corruption charges. Partly thanks to Mr. Silver, the Essex Crossing site — once known as the Seward Park Urban Renewal Area, or Spura — sat fallow for over four decades, its empty lots an open, nagging eyesore in a diverse, dense neighborhood. Mr. Silver had fought with the community over much-needed affordable housing, worried of losing his Jewish constituency.