It is perhaps the largest project ever proposed for Greenwich Village, and it has angered many residents in the area as few issues have recently. Opponents say the development would mar one of New York’s signature neighborhoods.

Now the project’s future has fallen on the shoulders of two high-profile politicians who aspire to become the next mayor — Christine C. Quinn, the City Council speaker, and Scott M. Stringer, the Manhattan borough president.

New York University says it needs more dormitories, classrooms, athletic and performance spaces and a hotel to accommodate its burgeoning student body and compete with national universities, and it wants to erect four buildings amid two sprawling apartment complexes north of Houston Street.

The square footage of the four buildings, the tallest of which would be 25 floors, would nearly equal that of the Empire State Building.