The Bloomberg administration is scrambling to gather enough City Council votes to enact the mayor’s final plan for reshaping New York City’s skyline with a new generation of ever-taller skyscrapers.

The proposal would rezone a 73-block area surrounding Grand Central Terminal and allow the kind of sleek skyscrapers the administration says are necessary for the city’s premier office district to stay competitive with London and other world capitals. In some locations, developers would be able to erect towers more than twice the size of current buildings, which would cast the Chrysler Building, the Waldorf-Astoria and St. Bartholomew’s Episcopal Church into shadow.

Many leading figures in the real estate industry, and many construction unions, support the plan, as does the Regional Plan Association, an influential private research organization. But a broad array of Manhattan community boards, preservationists and elected officials contend that the rezoning has been rushed, and could overwhelm a neighborhood whose streets are already congested and subway lines overcrowded.

The City Council will have its first hearing on the proposal on Tuesday, and is expected to vote on it within the next month. In pushing through more than 125 rezoning proposals throughout the city, Mayor Michael R. Bloomberg has usually overcome the obstacles inherent in passing such changes. But with fewer than 75 days left in his term, the political dynamics have changed. The mayor’s clout with the Council is fading. His onetime ally, Christine C. Quinn, the Council speaker, is also a lame duck.