Senators Clinton and Schumer and the speaker of City Council, Christine Quinn, are putting pressure on the Metropolitan Life Insurance Company to accept a tenant-backed bid to purchase Stuyvesant Town and Peter Cooper Village over higher offers.

According to sources familiar with the bidding process, the senators and Ms. Quinn have called the chairman of Met Life, C. Robert Henrikson, asking him to give special consideration to the tenants’ bid.

Yesterday was the deadline for prospective buyers to submit bids to Met Life for the 110 buildings on Manhattan’s East Side. The potential sale, which would be the biggest in the city’s history, has generated widespread interest from the area’s biggest developers, and bids are expected to reach $5 billion.

Met Life will ask a group of finalists to submit another bid by October 15, and could close on a deal by November 15, according to the New York Times.

A spokesman for Met Life, John Calagna, would not comment yesterday.

Mr. Schumer, Ms. Clinton, Ms. Quinn, and host of local elected officials have said they fear that a sale would permanently alter the character of Manhattan and serve as a loss of critical affordable housing.

Currently, about 70% of the apartments are rent-regulated under state law, and about 30% are rented at market rates. Over time, many of the rent-regulated apartments will become market rate under the existing law, but some tenants and public officials fear that a multibillion-dollar sale would motivate a new owner to accelerate that gradual process.

The local City Council member, Daniel Garodnick, helped put together a tenant-backed bid in coordination with the Stuyvesant Town and Peter Cooper Village tenant association and an army of real estate and finance professionals.The bidders want to give existing tenants an opportunity to buy their apartments at affordable rates, and they want to maintain some apartments as affordable rentals.

The Bloomberg administration has said it is considering its options, but has not come out and backed the tenants.

Yesterday, Mr. Garodnick would not disclose the value of the tenants’ bid, but he said the group had partnered with “major real estate firms and financial institutions.” He said the bid included no public subsidies.

“This was not a bake sale effort,” Mr. Garodnick said. “The tenant group has been able to amass a major source of capital to be able to control their own destiny.”

If the bid fails, council members have said they will consider pushing for legislation.

Real estate lawyers say that Met Life is not legally bound to accept the highest bid, but as a public company it has a fiduciary responsibility to shareholders to sell it to the best bidder.

The offices of Mr. Schumer and Ms. Clinton would not comment yesterday.