In an effort to jump-start state lawmakers’ stalled budget negotiations, Gov. Dannel Malloy on Tuesday offered a major compromise, cutting in half his proposed shift of teacher pension costs from states to municipalities.

Connecticut has now missed its July 1 budget deadline by more than two months, making it one of just two states without a budget for fiscal year 2018. Even after the ratification in late August of a $1.5 billion state-employee concessions deal negotiated by Malloy, the state faces a projected $1.6 billion deficit in fiscal year 2018. Over the next two fiscal years, that number will rise to $3.5 billion.

The governor’s original budget would have required cities and towns to pay $400 million of teachers’ $1.2 billion annual pension bill, which, as of now, falls entirely on the state. Under Malloy’s new plan, municipalities would pay just $200 million, with the remaining $1 billion coming out of state coffers. Malloy told the CT Mirror on Tuesday that he hopes the compromise dispels the notion that he has been inflexible during the negotiations.

“This idea that we just put a budget out there and we won’t budge is not fair and is not appropriate,” he said. “We have repeatedly demonstrated a willingness to discuss things.”

In the Connecticut General Assembly, responses to the compromise among lawmakers on both sides of the aisle have been lukewarm.

Democratic Senate President Pro Tempore Martin Looney, D-New Haven, called the proposal a move in the right direction and said he remains optimistic that the House can pass a budget next week. But House Democrats rejected Malloy’s compromise in a closed-door caucus Wednesday.

“My caucus is not in favor of it,’’ Speaker of the House Joe Aresimowicz, D-Berlin, told reporters Wednesday. “The governor has clearly articulated it, that it’s a priority. We will talk to him and figure out what that looks like. … But it’s a hard issue in our caucus. Our caucus doesn’t necessarily like it or want to vote for it.’’

The debate over who should foot the teacher pension bill is part of a broader dispute over how the state and municipalities should share the fiscal burden. During negotiations, the debate pits an overwhelming majority of lawmakers from both parties against the Malloy administration.

Representative Dave Yaccarino, R-North Haven, said Republicans would like to see municipalities’ portion of the teacher pension bill reduced to zero.

“I don’t agree with any of that,” he said. “I don’t agree with that at all mainly because that’s not solving state budget issues. It’s just a temporary fix.”

Yaccarino added that Republicans are united against the proposal. He also estimated that 95 percent of Democrats are opposed.

In an interview last week with the Hartford Courant’s editorial board, Malloy said he didn’t think the House was “anywhere near passing a budget that I could sign.” And Republican Senate President Pro Tempore Len Fasano ’81, R-North Haven, told the News on Monday that he sees no path to a resolution.

Until lawmakers reach an agreement, the state will continue to be funded by an executive order signed by Malloy on June 30. That order declared a fiscal emergency and appropriated funds to support the “essential functions” of state government. The bare-bones interim plan relies on deep cuts to municipal aid and social services.

Even under the governor’s austerity measures, though, the state is on track to run a $94 million deficit this fiscal year, according to a monthly report published on Aug. 21 by the Malloy administration.

While lawmakers deliberate, the clock is ticking for the state’s municipalities. Come October, states will have to go without their regular state aid payments, if the governor has still not received and signed a budget from the legislature, said Chris McClure, secretary of the Office of Policy and Management. For small towns that lean heavily on state funds, that could mean insolvency is just a few months away.

The House is scheduled to vote on Democrats’ proposed budget on Sept. 14.

Jacob Stern jacob.stern@yale.edu | @jdkstern13