MANCHESTER — City teachers have overwhelmingly rejected contract modifications touted as saving the jobs of 143 teachers.

The 143 positions are among the 161 school employees who have been told they can expect to lose their jobs when school ends in June.

Union President Ben Dick said the Manchester Education Association (MEA) membership voted to reject the proposal by a 3-1 margin.

“It should never have been the sole option” for saving teachers jobs, Dick said.

With the proposed contract concessions rejected, the MEA will lobby aldermen for more money for the schools.

“We still have the ability to receive a budget that is above the budget proposed before,” Dick said.

“I’m sad,” said Mayor Ted Gatsas. “I think that everybody had the ability to participate in a solution that would have saved jobs. At this point, I don’t have an answer for everybody, but I feel sorry for the 161 teachers who are going home.”

Union members were promised that the 143 jobs would have been saved if the contract changes were approved and 50 teachers at the upper end of the pay scale agreed to accept an enhanced retirement package that was part of the proposal.

The contract modification included concessions on employee health care benefits and costs. Teachers would have faced higher co-payments and deductibles for some services that could have led to out-of-pocket costs of up to $200 for members opting for an HMO. Members who opt for a point-of-service plan and use out-of-network providers would have seen the out-of-pocket cap jumping from $1,500 to $1,800 a year, according to an analysis prepared by the MEA.

While potential layoffs would hit junior members of the teaching staff hardest, Dick said support for the proposal did not seem to come from teachers at any particular level of experience.

In addition to lobbying the Board of Mayor and Aldermen for more money, the teachers union will try to make its case with the public.

“We can continue to do what we have been doing, which is to share what the proposed budget will do to our children, the children of Manchester,” Dick said.

Aldermen last week split 6-6 on the issue of overriding the city’s tax cap to provide more money for schools. Gatsas said he doesn’t think supporters of an override can muster the 10 votes required to make it veto-proof.

Property owners who think they can handle higher taxes will have a chance to vote with their checkbooks when they get their tax bills, which are due out soon.

“There will be something in their bill this week that they can send a check to the school district,” the mayor said, referring to a voluntary contribution program. “That would certainly be support for the school district.”

A legal opinion by the New Hampshire Retirement System on Wednesday afternoon would eat into the potential savings from the early retirement incentive.

One provision in the deal rejected by the teachers would have required any teacher who accepted a proposed $13,000 retirement incentive to pay both the school district’s and the employee’s portion of retirement costs to the NHRS. NHRS attorney Timothy Crutchfield told Superintendent of Schools Thomas Brennan on Wednesday that the stipulation violates state retirement law.

“Attorney Crutchfield indicated that the language in the tentative agreement was vetted by in-house counsel and outside counsel, and it was determined that the language would not be allowed,” Brennan wrote the school board on Wednesday.

The NHRS decision could have cost the school district $78,000 in additional severance.

If the opinion stands, it also could have an impact on newly signed union contracts with city unions. The police, fire and other department unions include an early retirement incentive, as well as a stipulation that the retiring employees pay both portions of the NHRS payments on the severance bonus.

The Manchester Association of Police Supervisors contract, for example, says that the “city may withhold from this benefit such amounts as are necessary to pay the employer and employee contributions to the New Hampshire Retirement System.”

Although it is not written as a requirement, Gatsas said there have been retiring police who have paid both fees.

The city has not budgeted money for the cost at this time, said Gatsas.

With the contract addenda rejected, the mayor said the city will now try to figure out the implications for the 2013-14 school year, and he said the city’s financial situation will be an issue for discussion when the teacher contract expires next year.

“I think the contract now is totally open,” Gatsas said. “I’m sure we would have to be looking at proposals that would take into consideration the money we would need to bring back teachers.”