New York — New York State politics -- no stranger to quarrels, policy reversals, and shifting alliances -- may outdo itself in the race for governor this year.
On the surface, it looks as though New York City Mayor Edward I. Koch is the front-runner this year. Polls show the outspoken, feisty mayor is easily the most popular Democrat in the Empire State, despite some poorly timed criticisms of life in the suburbs which he made during a widely publicized interview recently.
But the political pot is boiling below the surface.
Item: Former President Jimmy Carter may play a key role in New York's gubernatorial campaign this year, supporting Democratic Lt. Gov. Mario Cuomo, who is running against Mayor Koch in the Democratic primary.
Item: Some Koch strategists joke that their candidate may get President Reagan's endorsement. On a recent trip to New York City, the President said Mr. Koch would make a ''good governor.''
But, normally, Republican presidents support Republican candidates -- and, indeed, the word from the White House several months ago was that Mr. Reagan, unhappy with Koch attacks on Reaganomics, would do everything he could to see a Republican elected.
Since then, however, New York State Comptroller Ned Regan, the man seen as the strongest Republican candidate, has pulled out of the race saying that Koch was too formidable an opponent. This left the Republican field barren of any candidate with even the moderate statewide ''name recognition'' that Mr. Regan had.
Former US Attorney Paul Curran and millionaire businessman Lewis Lehrman are the two leading GOP candidates to date. Mr. Lehrman has never run for public office before. Mr. Curran is a former three-term state assemblyman and gained some degree of fame as former State Investigation Commission chairman.
Compared with the highly visible, peripatetic Koch, by nature an irrespressible showman, the Republican choices seem eclipsed. And knowledgeable sources say the White House, wanting to back winners in this crucial congressional election year, may all but forget about the New York governor's race.
Yet Mr. Cuomo has repeatedly tried to tie Koch's apparently rising political star to President Reagan in an attempt to get more liberal Democrats to join the Cuomo bandwagon. Already, the lieutenant governor is virtually assured of receiving the state Liberty Party endorsement. In addition, Cuomo has gained the endorsement of some of the state's biggest labor unions, including the powerful 225,000-member Civil Service Employees Association of New York.
Meanwhile, former President Carter and Cuomo are scheduled to meet sometime this summer to determine the precise nature of Carter's support, according to the lieutenant governor. The two men became good friends when Cuomo ran Carter's 1980 presidential campaign in New York, while Koch continued to criticize Carter sharply.
Many political observers here don't see Carter's formal endorsement of Cuomo nor his possible active campaigning as an attempt by the former president to get back into active Democratic politics. Rather, they say, Carter's presence here could help turn a somewhat lackluster gubernatorial campaign into more of a horserace, especially as the Democratic primary approaches in September.