“I’m a man of faith, so I always pray,” Senator John Sampson, the leader of the Democratic conference, said just after noon as he walked past the sign. He had been asked if there was any prayer of reaching an agreement to bridge a roughly $3 billion budget imbalance. “We’re working hard. We’re working very hard.”

Here in the Capitol, a combination of prayer and hard deliberation gets you … a tentative budget agreement that solves no long-term problems, makes all parties to the accord unhappy and is almost certain to be litigated.

Mr. Sampson had just met with Sheldon Silver, the Entish speaker of the State Assembly. He did not say so, but after a four-week stalemate, he and Mr. Silver were ready to take a $2.8 billion deal package to David Paterson. It was the only thing Mr. Sampson could get his Senate Democrats—who hold a one-seat majority in the highly dysfunctional 32-member chamber—to agree to, and its apparent acceptance by the governor the evening of Monday, Nov. 30, ended a game of fiscal chicken that Mr. Paterson and senators had played for over a month.

The next morning, confusion reigned. The New York Post’s Fred Dicker played the Twilight Zone theme on his morning radio show. Bills that legislative leaders were expecting didn’t immediately materialize. Mr. Paterson went on the radio to say the legislators “want to get out of Albany by taking on half of the problem,” and the agreement “isn’t recurring and isn’t particularly real.”

No one knew if this was calculated bluster or genuine disagreement. Mr. Sampson went once again to Mr. Silver’s office, and said when he exited that “we have our staff working on a compromise.”

Finally, Mr. Paterson said at 11 a.m. that the argument had shifted over who would send what bill language when and in what form, but he was tied to the Legislature’s “last, best and final offer.”

“Look, the reality is that when John Sampson says, ‘I don’t have 32 votes for something,’ it’s no longer a negotiating tactic,” said a frustrated Senator Eric Schneiderman, a Manhattan Democrat who is one of Mr. Sampson’s top lieutenants. “Everybody, including the governor, has just got to accept that.”

Mr. Sampson is a bulky man who rations his words as if they were a precious commodity, and who arguably has the least enviable job in Albany. He is in charge of herding a factionalized group of Senate Democrats who have realized over the course of a year that any one of them can hold out for whatever they want until everyone else tires of the stalemate and gives it to them—the individual benefit trumping the collective good every time.

This time the issue was proposed cuts to school aid in the middle of the year, and according to conversations with several Democratic senators, the principal obstructionist was Long Island Democrat Craig Johnson.

“My position’s very clear: It’s about protecting the property taxpayer throughout New York State, it’s about protecting the children and our schools—private or public and the parents who send them and the grandparents who love those kids,” Mr. Johnson said on the chamber floor Monday, insisting that he is not just focused on his political well-being. (There are the children, but there are also the members and dollars wielded by the teachers’ union.)

“I’m being what I’m supposed to be, which is a state senator representing not just the seventh senatorial district, but the residents in New York State,” he said.

At first in private, and then publicly, Mr. Johnson drew his line in the sand. Others—including Brian Foley, Darrel Aubertine, David Valesky, Andrea Stewart-Cousins and Bill Stachowski—joined him. Republicans took the same position because, out of power, they could. (They were opposed to mid-year cuts to school aid last year, too, when they controlled the Senate.) Mr. Silver and his colleagues in the Assembly sat frustrated. The state was stuck.

For most of that afternoon, the Senate floor had been empty. In typical fashion, the deal was being hammered out by leaders in private. Senators had no legislation to consider, with Mr. Sampson huddling at the Governor’s Mansion on Eagle Street with Messrs. Silver and Paterson. Many members sipped cola or coffee taken from a members lounge. Two compared turkey brining techniques they had used over Thanksgiving.

In what one assumes is a very deliberately cultivated contrast to the unabashedly sluggish senators, Mr. Paterson has spent the last month trying desperately to convince voters, at high volume, that New York will run out of money if nothing is done. The state, with a budget of more than $130 billion, would have about $36 million in the bank by December’s end, he has said, repeatedly.

Mr. Paterson’s own political standing is low, and he has bashed the even-less-popular legislators to make himself look stronger, even soliciting campaign contributions in the process. He has made the case that while it is difficult, school aid must be cut to save money going forward. When this argument did not work, he asked the Legislature for the power to let him cut things himself—a roundly rejected, constitutionally dubious, fiduciary equivalent of the Gulf of Tonkin resolution.

“The Senate in particular doesn’t know that we’ve run out of time, or knows that we have run out of time and apparently is more concerned with the short-term politics than the long-term realities,” Mr. Paterson said on a Nov. 29 conference call with journalists. “Some of these senators said last week that they were not going to let me do their jobs. My question is: When are they going to do their jobs? Their job is not placating special interests and running back to their districts with their hands in the air saying, ‘Look what we didn’t cut.’”

The Senate had responded at various points with counterproposals, but the ideas have been fiscally loose at best and downright wacky at worst. The most outrageous have tended to come from Senator Carl Kruger, the slouching South Brooklynite who became chairman of the chamber’s Finance Committee after he corralled three other senators into a faction and strategically forced perks from the leadership.

He claimed at a press conference on Nov. 16 that $135 million could be realized in December by collecting taxes on cigarettes sold on tribal reservations. The idea, baffling even Mr. Sampson’s top staffers, dominated discourse for a week, and gave Mr. Paterson an excuse to bash the Senate for another week when, by private accounts, a deal was close at hand.

Mr. Kruger did not bother to attend Monday’s session. He instead sat two floors below the chamber, conspicuously enjoying lunch with his “amigos”: Senators Hiram Monserrate—who is due in court this week to be sentenced for an assault conviction—and Ruben Diaz Sr., who contributed to the stalemate by staying in his Bronx district to distribute turkeys rather than come to Albany.

“It’s a game!” Mr. Diaz said.

“There’s more than adequate common ground where we could have closed this down two weeks ago,” Mr. Kruger said, seriously.

They shuffled upstairs. Messrs. Sampson and Silver returned from the Governor’s Mansion, having secured Mr. Paterson’s agreement to a package of deficit reduction that contained $2.8 billion of fund sweeps, one-shot allotments and cuts to state agencies and health care. Mr. Silver told his members of the deal in a closed-door session around 6:30 p.m. Monday, the members said. Mr. Sampson told Mr. Kruger, as well as Senators Jeff Klein, Liz Krueger, Pedro Espada Jr. and Malcolm Smith, in a smaller room. Mr. Kruger, someone familiar with the meeting said, was especially giddy.

On Tuesday, after the tentative agreement was reached, Mr. Paterson proclaimed himself dissatisfied. He insisted that he might still delay some payments for school districts because the legislators hadn’t gone far enough in cutting spending. But whatever—he wasn’t going to get anything more, and seemed sick of the stalemate.

“It does give us about $600 million in cuts, and some other measures that require legislative approval,” Mr. Paterson said. “So we will not cut off our nose to spite our face.”

jvielkind@observer.com