Democrats won big races in the Northeast, and a backlash against Reaganomics is being given a lot of the credit. In New York, Democratic Lt. Gov. Mario M. Cuomo narrowly defeated millionaire businessman Lewis E. Lehrman to become the state's first Italian-American governor. The race appears to have been the closest New York gubernatorial race since 1954. He was nudged over the top largely by a 2-to-1 lead in heavily Democratic New York City. Mr. Lehrman, who offered a state economic program modeled after President Reagan's 1980 tax-reduction package, was one of the biggest spenders nationwide in this election. He called for a vote recount, but made no charges of wrongdoing.In New Jersey, however, big spending apparently helped Democrat Frank Lautenberg, a millionaire businessman and political neophyte, score a slim victory over GOP US Rep. Millicent Fenwick. Mr. Lautenberg, a founder of Automatic Data Processing Inc., which employs 4,000 people in New Jersey, waged an expensive campaign linking the popular Mrs. Fenwick with the President's economic program.The colorful four-term congresswoman said the major reason she lost was that so ''many people are out of work or fear they will lose their jobs.'' Lautenberg attacked her record of voting for cutbacks in federal jobs programs and college loans.While Cuomo squeaked by Lehrman in the New York gubernatorial race, incumbent US Sen. Daniel Patrick Moynihan scored a whopping victory over Assemblywoman Florence Sullivan. Mr. Moynihan claimed his win was a vote against Reaganomics; most observers say Mrs. Sullivan's poorly financed campaign never really had a chance.Pennsylvania's two major races, by contrast, were won by incumbent Republicans with strong records of accomplishment in the state. Gov. Dick Thornburgh's victory over his Democratic challenger, US Rep. Allen E. Ertel , is credited largely to his efforts to clean up corruption in the state. US Sen. John Heinz, who called for a ''midcourse correction'' in Reaganomics and won support even of state labor unions, easily won reelection.