Lawmakers in Albany say they may be close to passing a budget.
9 bills need to be voted on to approve it, and state senators will be in session through the night to push them through.
The State Assembly will be back to vote Wednesday.
Sources said Gov. Andrew Cuomo has given a message of necessity, which means that the three-day waiting period for lawmakers to properly assess the bill would be waived.
Assembly leaders say they hope a proper budget will pass sooner rather than later.
"School districts need to have certainty as to what their education budgets are; those are due May 1st," Assembly Speaker Carl Heastie said. "So I think we should try to give them as much clarity and, I'd say time, to get their school budgets done."
Monday, lawmakers passed an "extender" for the previous budget, which will keep the government running through the end of May.
As part of the new budget bills that will be passed, the State Senate and Assembly will repeal the extenders.
It has been a grueling negotiation, with lawmakers working through last weekend, but the situation improved Tuesday.
"Obviously. I mean, I've talked about the fact that this has been extremely dysfunctional," said Andrea Stewart-Cousins, the State Senate Democratic Conference leader. "It's gone on, and on, and on.
"I think the people of New York are expecting us to get a budget, to do our jobs, and I'm hoping we will be able to do that."
But it was not easy, even on the final day. After a meeting with Cuomo on Tuesday morning, Heastie stormed out of his office, but promised to pass the bills, some of which he and his members do not particularly like.
"If it's what we just talked about downstairs, send them and we'll pass them," Heastie said. "So I just need to put that in because, who knows, he could put something else that we didn't discuss.
"I'm not going to let the Assembly get blamed for no budget. Send the bills."
But a few hours later, Cuomo, who tended to a barge accident in the Catskill region, seemed to throw cold water on the idea of getting the budget resolved quickly.
"We will work out these issues out when we work them out. My guess is we will work them out after what they call the Easter break, which is coming now," the governor had said. "So the legislature will go back to their districts for a couple of weeks, and I think we will get it done then."