The deal was announced Thursday by Gov. Andrew Cuomo at his East Side office.
TWU Local 100 President John Samuelsen wrote Cuomo Tuesday night, asking him to intervene in the negotiations and effectively close the deal.
The package on the table would require new hires to work for five years before reaching the top raise of 8%, a provision that would help save the MTA money.
The five-year deal needs approval by union members and the Metropolitan Transportation Authority board.
Cuomo says it's a fair agreement for TWU Local 100's 34,000 transit workers, and he's underscoring that it would not require fare hikes.
Under the terms of the agreement, TWU workers would receive increases within the 2% cap that Governor Cuomo has achieved with state labor contracts (1% increase in each of the first 2 years, beginning with 2012, and 2% increases in the last 3 years).
Employees would pay an increased share of health care costs, increasing from 1.5% to 2% percent of the employee's salary, but would receive important new benefits including paid maternity/paternity leave, coverage of health care for surviving spouses of deceased TWU retirees, and improvements to dental and optical benefits.
The contract will have no impact on MTA fares and will be accommodated within revisions to the MTA financial plan.
The tentative agreement is subject to approval by the TWU Local 100 executive board and ratification by the membership, and subsequent approval by the MTA board.
(The Associated Press contributed to this report)