HARTFORD — State leaders gathered in lame duck session on Monday to close Connecticut’s estimated $350-million budget gap for the current fiscal year.

In negotiations characterized by Speaker of the House James A. Amann as going “surprisingly, extremely well,” lawmakers were able to agree on a deficit mitigation measure that will close the current deficit without raising taxes, laying off state employees or dipping into the state’s “rainy-day fund.” The measure, first proposed by the Gov. M. Jodi Rell in October, received overwhelming support in both houses of the General Assembly, unanimously passing the Senate with only one dissenter in the House.

But even as legislators congratulated each other on the successful passage of the bill, they warned that a far more challenging fiscal situation looms on the horizon. The state Office of Policy and Management projects that the state is facing a $6 billion deficit through 2011.

“This is the first step in a much longer process,” said Senate President Donald E. Williams in an interview with the News. “[Next year] there won’t be a single department or agency that goes untouched.”

Amann, who is retiring in January to run for governor in 2010, warned that the next budget cycle would be “ugly,” while State Sen. Toni Harp of New Haven said there will be some “excruciating” cuts to state services.

“I think the next General Assembly will face something barely better than what I faced my freshman year,” Amman said, referring to the over $1-billion dollar deficit facing the state in the 1990-’91 session, which comprised a larger percentage of the overall budget than does the current shortfall.

According to many here at the Capitol, the situation is now even direr. The state weathered the last crisis, for instance, by taxing income for the first time in its history, a resource it no longer has up its sleeve. State leaders like Williams and Amann say they hope President-elect Barack Obama’s administration will be more receptive to state concerns. They have both reached out to the Connecticut Congressional delegation for help from the federal government.

Sen. Joe Lieberman ’64 LAW ’67, for his part, spoke to reporters Tuesday about federal help to states. He said 41 states are reporting budget deficits warning of harm to vital state services. He proposed an increase in the Community Development Block Grant funding and the Federal matching rate for state Medicaid expenditures. Combined, he said, his plan would generate at least an additional $250 million for Connecticut.

Compared to neighboring states, Connecticut is standing up surprisingly well. Gov. David A. Paterson of New York proposed over $5.1 billion in cuts to Medicaid and education funding.

Republican Senate Minority Leader Len Fasano ’81, who represents East Haven, North Haven and Wallingford, said healthcare funding is a “sacred cow” and would only be cut in the worst of situations.

Harp said such cuts are counterproductive.

“We can’t lose sight of the fact that we will come out of this,” she said. “We need to make sure we come out of this stronger than we went in. Cutting basic social services would be a big mistake.”

Amann agreed, saying the state needs to be extremely careful where to invest and where to cut. Citing the recommendations of economic experts consulted by the governor and the legislature, he said the worst thing the state could do is cut funding for infrastructure, education or social services.