New York Gov. David A. Paterson has persuaded state lawmakers to cut spending by $1 billion over the next year and a half, a deal that includes cuts in aid to hospitals that will probably be in excess of $200 million over the next 18 months when federal matching funds are included. The issue of how to cut healthcare funding was one of the major sticking points that held up negotiations, lawmakers briefed on the talks said. Funding levels for hospitals proved particularly difficult to resolve because the Paterson's plan called for greater cuts than the healthcare industry and many lawmakers wanted.