Governor Paterson and lawmakers are racing to complete a budget that they say will add hundreds of millions of dollars in health care and public school aid above what the Spitzer administration had proposed in January, and will raise taxes on cigarettes and online shopping.

Mr. Paterson, a former lieutenant governor who jumped into the complex negotiations just two weeks ago when he replaced Eliot Spitzer as governor, and legislative leaders emerged from closed-door talks yesterday evening with a budget in sight, but with hopes fading that they would complete the budget before the constitutional deadline: the end of today. Lawmakers said they would begin today to crank out the 5,000 pages of budget bills and start voting on them. The process could extend to as late as Wednesday.

“It’s a mechanical problem, you’re always racing against the clock in budget negotiations, but this time we’re racing together against the clock,” Mr. Paterson said, according to the Associated Press.

The budget appears to stand at $124 billion, about $200 million less than what Mr. Spitzer proposed in January. The tentative deal calls for raising spending $500 million beyond what Mr. Paterson advised this month, a total funds increase of 4.8% over last year’s spending levels.

The increase comes amid warnings of a recession and expectations that state revenue will shrink further, threatening to create midyear deficits.

To help close what is already a $5 billion budget gap, lawmakers are set to approve an increase of the state cigarette tax to $3 a pack, bringing the total tax in New York City to $4.50, the highest in the nation. They are also expected to change the tax code so that Amazon.com and other online retailers are required to charge state and local sales taxes on all purchases from New York.

Lawmakers are expected to add more than $300 million in school aid to the education budget Mr. Spitzer, who resigned from office earlier this month over a prostitution scandal, had proposed, delivering more to money to Long Island and New York City schools. They also will tack on $245 million for Medicaid and other health spending. The bulk of it will go to Medicaid restorations for hospitals, nursing homes, and home care, and pharmacies.

Early Sunday, budget talks appeared to grind to a halt, as lawmakers in various subcommittee meetings struggled to balance the numbers and cut their conferences short. The speaker of the Assembly, Sheldon Silver, who missed a flight while en route to Albany yesterday, did not show up at the Capitol until the afternoon. Much of the disagreement centered around the $1 billion that the governor and lawmakers said last week was available to smooth over cuts to health care and education.

While all sides agreed that several hundred million dollars of the total would be generated by taxes and fees, lawmakers yesterday clashed over how to raise the revenue. Interest groups targeted by various proposed taxes and fee increases that gained support in the Legislature mounted a weekend lobbying offensive that caused divisions in the Senate, some of whose Republican majority members resisted a plan to double the state cigarette tax or raise taxes on health plans.

A scattering of Republicans suggested reviving the Assembly idea to raise more than a $1 billion in revenue by slightly increasing income taxes on millionaire residents. That tax hike proposal is “not dead,” a Republican senator said yesterday afternoon, “but it’s breathing damn hard.”

Senate Republicans also appeared to defeat a health care proposal developed by the Spitzer administration that called for overhauling inpatient reimbursement rates so they better reflect hospital costs. Lawmakers agreed, however, to shift about $100 million in state Medicaid money to primary and preventive care from inpatient care.

Most of the $1 billion that lawmakers agreed to spread around ended up in education and health care, leaving other areas in the budget facing stiffer cuts.

In the past, lawmakers have passed emergency spending bills when they missed budget deadlines to keep government running.

The sudden resignation of Mr. Spitzer and assumption of power by Mr. Paterson two weeks ago wreaked havoc on a budget process that is usually a last-minute sprint even without such drama. For different reasons, the new governor and lawmakers felt compelled to cobble together a spending plan despite the prohibitive time frame.

“Appropriate steps will be taken to ensure that government continues,” a spokesman for Mr. Paterson said.

Mr. Paterson, whose personal indiscretions and questionable use of state and political funds have come under scrutiny, faces tremendous pressure to demonstrate his fitness for a job to which he was not elected. Lawmakers, who have their re-elections to worry about this November, are eager to show that the gridlock during the tumultuous Spitzer era was not of their making but the fault of an abrasive governor.