Gov. Dannel Malloy’s administration and state labor unions began closed-door negotiations Wednesday that Malloy hopes will result in budget savings of $2 billion over the next two years.

In order to close the state’s $3.3 billion budget deficit, Malloy said in his budget address Feb. 16 that he wants state employees to give up $1 billion per year over the next two years in the form of wage freezes, changes to their health plans and adjustments to the retirement age, among other savings. The details will be worked out in negotiations with union representatives over the coming months, but Malloy’s $2 billion goal will face tough opposition.

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The officials in the Malloy administration and union leaders said they would not air their differences in the media, releasing a cautiously optimistic statement after their first meeting Wednesday night.

“We engaged in a respectful and frank discussion,” wrote Deputy Budget Director Mark Ojakian and Dan Livingston, chief negotiator of the State Employees Bargaining Agent Coalition. “We agreed to continue meeting and that the substance of our meetings would not be discussed in the press. We hope these discussions will be productive and yield positive results.”

Still, several union leaders have complained that Malloy is not striking the right balance between sacrifices by state workers and increased taxes on the wealthy. In Malloy’s budget proposal, income taxes on the state’s wealthiest residents would rise by 0.2 percent.

Larry Dorman, a representative of Council 4 of the American Federation of State, County, and Municipal Employees, which represents 17,000 of the state’s 45,000 employees, said Malloy’s budget proposals disproportionately burden the middle class.

“It’s simple math: if you’re talking about a billion dollars per year, that means you’re asking state workers to find over $20,000 in their pockets to help close the deficit,” Dorman said, adding those making over $1 million a year were not being asked to sacrifice much. “I hope we can address that inequity.”

At a packed town hall meeting in New London Wednesday night, Malloy said he would not raise taxes by any more than the $1.5 billion he has proposed — already the largest total tax increase in the state’s history.

If the $2 billion in labor savings are not found, Malloy said, he may have to lay off thousands of workers and gut the social safety net for the state’s poorest.

“We don’t have a lot of options in Connecticut,” Malloy told The Hartford Courant Wednesday. “I have not hidden the fact that in the absence of success, we’ll have to go down a different road [for more budget cuts] and we’ll be prepared to go down that road if we must.”

A sign that Malloy may be less than confident about reaching his goal on concessions came last week, when he drafted a bill that would expand his authority to make emergency midyear budget cuts.

If the bill passes, Malloy will have the authority to unilaterally cut $280 million from state grants to local government budgets, including New Haven’s.

Malloy’s ambitious effort to win labor concessions is partially handicapped by a decision he inherited.

In 1997, former Gov. John Rowland negotiated a 20-year contract with state employee unions. The provisions governing health benefits and pensions will remain in effect until 2017, forcing Malloy to look to other savings, such as wage freezes and retirement age adjustments, to find the money he is requesting.

State Rep. Roland Lemar, a former Ward 9 Alderman, said cooperation between state employee unions and the administration is crucial to the state’s future fiscal health.

“No one is happy right now, everyone wants someone else to pay, but if we don’t address the deficit honestly, we’re only delaying the inevitable and making it more painful down the road,” he said.

The New London town hall meeting was the third of 17 that Malloy plans to hold throughout the state to pitch his budget proposals to the public. His New Haven stop is scheduled for March 23.