The New York Republican Party, which once proudly gave the state Theodore Roosevelt, Thomas E. Dewey and Nelson Rockefeller, is on the verge of giving it — well, nobody.

Five weeks before Election Day, Republican candidates trail in polls for every statewide race on the ballot, risking their first complete shutout since 1938. The party’s best hope this year, attorney general candidate Jeanine Pirro, last week managed to dominate headlines for the wrong reason: She confirmed she is under criminal investigation for considering bugging her husband, whom she suspected of having an affair.

Meanwhile, Democratic Senator Clinton is so far ahead in polls that most comment about her centers on a possible presidential race in 2008. And Democrat Eliot Spitzer is similarly running away with the race to succeed Republican Governor Pataki, who isn’t running again.

“The Republican Party today is in a state of chaos,” said former Senator D’Amato, 69, its most powerful figure while in office. Mr. D’Amato says the party’s eclipse — as recently as 1998, it held the governorship, the attorney general’s office and a U.S. Senate seat — results partly from opportunities it missed while in power.”The party became atrophied in the 12 years that George Pataki was governor,” he says. “We didn’t work to develop the bench strength.”

It also reflects trends going back decades — to demographic shifts that have eroded Republicans’ traditional base, and to ideological schisms dating back to the 1960s.

Once upon a time, there was no more vigorous font of Republican ideas and energy in the nation. New York Republicans in the 19th and much of the 20th century represented a desire for zealous reform of a political system dominated by the powerful and corrupt New York City Democratic machine known by the name of its headquarters building, Tammany Hall.

The spirit was captured by such figures as Mr. Roosevelt, governor from 1899 to 1900 and later, as president of the United States, who took on big business to curb monopolistic abuses.

Mr. Dewey, best remembered today for being the loser in the biggest presidential upset in American history, was the Rudy Giuliani of his day — parlaying his reputation as a rackets-busting prosecutor into three terms as governor from 1943 to 1954 as well as the presidential nominations in 1944 and 1948.

Then came Mr. Rockefeller, scion of one of the nation’s wealthiest families. Elected governor a record four times, he promoted civil rights and social-welfare programs.

The seeds of the Republicans’ current malaise were sown under Mr. Rockefeller, observers say. With Tammany’s demise, state politics shifted from issues of reform versus machine to a more ideological focus. Mr. Rockefeller’s brand of liberal Republicanism, increasingly out of step with a national party turning more conservative, began drawing more criticism even in New York.

Since 1974, a year after Rockefeller left Albany, no Republican has won statewide without the support of the tiny Conservative Party, whose power lies in its ability to split the conservative vote if Republicans nominate someone not to its liking.

The problem for Republicans is that while conservative clout was rising within the party, it was waning statewide.

Looking at the current state of the Republican Party, Joseph Mercurio, a political consultant who has worked for both Republicans and Democrats, said economic hard times have squeezed upstate New York, the Republicans’ traditional base, while “downstate you’ve picked up more Hispanics, more women,” Mr. Mercurio said. “The suburbs and exurbs where the Republicans used to dominate are more Democratic.”

“The state’s demographics have changed,” said Mr. D’Amato. The Democratic registration edge has increased from about 800,000 when he was elected in 1980 — after bumping off Rockefeller Republican Jacob Javits in a primary — to 2.3 million now.

This year, Conservatives and like-minded Republicans chose John Faso, a former Assembly minority leader, for governor, and John Spencer, a former Yonkers mayor, to challenge Mrs. Clinton. Mr. Spitzer leads Mr. Faso more than 3 to 1 in polls, while Mr. Spencer trails Mrs. Clinton by 2 to 1.

Mrs. Pirro, the former Westchester County district attorney, had been doing a bit better in polls — trailing Democratic nominee Andrew Cuomo, the former U.S. Housing and Urban Development secretary and son of former Governor Cuomo, by 14 points.

But that was before last week’s news that she had talked about placing an electronic eavesdropping device on a boat her husband used.

At the moment, the Republican Party is “in the worst shape in my living history,” said Mayor Koch, 81. “I’m elated in one sense, as a Democrat,” he said. “But it’s not good for democracy.”