NEW York State's three top political leaders are in the final rounds of their long fight to solve their budget crisis - or "the New York nightmare," as Vice President Dan Quayle refers to it.The hole in the current $30 billion-a-year state budget - second largest in the nation - is a wide $875 million. Another shortfall of at least $3.6 billion is expected in the new budget which begins April 1. The state's economic situation is "clearly the worst it's ever been," says Joseph Zimmerman, a political scientist at the Rockefeller College of Public Affairs. Gov. Mario Cuomo, who insists he could not "in good conscience" make a run for the White House if the deficit talks collapsed and no plan were in place, wants swift action. He says New York's credit rating, third lowest in the nation, is at risk. He has been negotiating intensively for weeks with Assembly Speaker Mel Miller (D) and Senate majority leader Ralph Marino (R). "The staffs are now working around the clock," says a Miller aide. The leaders agree that a multiyear solution that also includes next year's expected deficit is best. They do not agree on where to make the deepest cuts. Any plan they settle on must be approved by the Democratic Assembly and Republican Senate, moves that could come as early as next week. The pressure to act - including a new "just do it" ad campaign launched by a business lobbying group - is coming from all sides. Spending on social services, up sharply and now accounting for more than half of the state's budget outlay, is at the heart of the political fight. As his price for agreeing to a multiyear approach to cutting the deficits, Mr. Marino wants deeper social-service cuts than Democrats so far have been willing to accept. On Wednesday he outlined a plan to cut Medicaid and welfare spending by $1.6 billion over the next six months. Advocates for the poor promptly called it welfare bashing. Governor Cuomo says if the leaders cannot agree soon on a multiyear plan, the Legislature must approve the plan he proposed two weeks ago to close the gap. That package, widely seen as a move to force the multiyear approach, called for $214 million in social spending cuts and $265 million in school aid cuts. Many legislators, particularly Republicans, and education groups were incensed. They said that school districts had already absorbed major midyear cuts last December in a similar crisis. "As far as the Senate is concerned, school aid cuts for this year are out," insists Justin McCarthy, a spokesman for Marino. "When the Assembly is ready to buy into our Medicaid programs, we're ready to go." Assemblyman Miller, negotiating even as he awaits a jury's verdict on fraud charges in an investment venture, agrees that midyear school-aid cuts are unacceptable. Yet he says the Senate Republican proposal hits the poor too hard. Democrats are willing to accept a $1 billion cut in social spending, but the impact of their Medicaid cuts would fall harder on health-care providers. Miller also says the Republican plan overestimates the value of many of the cuts and focuses too singularly on Medicaid. "There can be no sacred cows," he says. New York City Budget Director Philip Michael says some Albany legislators have miscast the Medicaid issue as a New York City welfare problem. He says that 70 percent of Medicaid funds go for long-term care for the elderly and disabled and that Medicaid costs are rising much faster in upstate counties than in the city. One reason legislators may adopt a multiyear approach, says Jay Hershenson, vice chancellor of the City University of New York, is the poor reputation they have with voters for passing several recent budgets well after mandated deadlines. Since all Assembly and Senate members are up for reelection next year, both parties have an incentive to reach an early agreement, he says. Cuomo, who says he has no trouble making decisions but does not lightly leave commitments behind, technically would be free to declare his candidacy once an agreement emerges. New York's budget experience could be considered heavy baggage to carry in any race. However, the governor, if he runs, is widely expected to plead powerlessness in the midst of recession and point to New York as an object lesson. "I think his answer will be that this is not a Cuomo problem - this is a national problem," says Demetrios Caraley, a political scientist at Barnard College, "and that what the governors are doing now has been rendered irrelevant by the national economy."