The developments have created a sense in Albany that Mr. Cuomo is consigning fracking to oblivion. The governor has been influenced by the unshakable opposition from a corps of environmentalists and celebrity activists who are concerned about the safety of the water supply. The opponents include a number of people close to the governor, including Robert F. Kennedy Jr., a longtime environmental activist in New York whose sister is the governor’s ex-wife.

The fracking issue is the biggest environmental question, and the most polarizing, facing Albany, and New York’s decision is being closely watched nationally, as President Obama and Mitt Romney have both expressed support for increased use of natural gas as a means to reduce the nation’s dependence on foreign oil. The natural gas industry has been eager to drill in the Marcellus Shale, a deep underground repository that runs through West Virginia, Ohio, Pennsylvania and New York. Extraction there was too complex and costly until the advent of hydrofracking.

The debate is politically complex for Mr. Cuomo, who has established a record as a social progressive and a fiscal centrist. Mr. Cuomo has been interested in fracking because of the promise that it could bring jobs to an economically struggling region of the state. The industry has also been a prolific campaign donor, and rejecting fracking would risk Mr. Cuomo’s close relationship with The New York Post, which has strongly advocated for drilling.

But opposition to fracking has become such a touchstone for liberals that approving it, even in a limited fashion, would undoubtedly alienate some of his most dependable supporters. Anti-fracking protesters have shadowed Mr. Cuomo for months, at his home, his office, and his speaking engagements, and a wide array of celebrities, including Lady Gaga and Yoko Ono, have mobilized to express opposition to the technology.

“Andrew has a very good political antenna, and we’ve never seen anything like this in terms of grass-roots power,” Mr. Kennedy, whose father was a United States attorney general, said in a telephone interview. “In 30 years, I have not seen anything come close to this, in terms of the mobilization of the grass roots. You’ve got 20,000 people in the state who consider themselves to be anti-frack activists. So I think that’s got to impact the political process all around.”