Senator Schumer refused to guarantee yesterday that he would serve out six full years if he is re-elected next month, leaving the door open to a possible gubernatorial run in 2006.

Speaking during a televised live debate, Mr. Schumer was asked to answer “yes” or “no” to the question of whether he would serve his full term

should he be re-elected in November. He demurred and said he could “Never say never.” There has been speculation that the Democrat, who is a former state legislator from Brooklyn and has amassed a huge campaign treasury, may seek to replace Governor Pataki when the Republican’s third term ends.

His comments come at a time when New York’s senior senator is far and away the front-runner for a second term. The most recent opinion poll by Quinnipiac University, taken last month, showed Mr. Schumer with the support of 61% of registered voters interviewed, compared to 13% for his Republican challenger, Howard Mills, an assemblyman from Orange County, and 9% for the Conservative in the race, Marilyn O’Grady, an ophthalmologist from Garden City, Long Island.

The three candidates discussed tax cuts, Iraq, the war on terror, the Middle East, and energy prices, among other subjects, and while the debate made clear that the trio disagreed on nearly every issue, Mr. Mills and Dr. O’Grady struggled to make a case for why Mr. Schumer should be voted out of office.

Mr. Mills said he supported the war on terror and conceded that Mr. Schumer had been tough on terror in his votes since the September 11 attacks.

“Prior to 9/11 he has a long record of voting to cut the military or voting to cut intelligence gathering services like the CIA,” Mr. Mills said. “All wrong choices. All things that help to lead to a situation in which we were vulnerable to situations like 9/11. Saddam Hussein was a terrorist. He was paying thousands to homicide bombers who were going into Tel Aviv and blowing up innocent people.”

Dr. O’Grady, who during the closing statements of the debate lost her train of thought and had to stop her statement and restart it minutes later, called the war in Iraq the “right thing to do” and said, “I am happy that they are fighting terrorists over there rather than fighting them here in Times Square.”

Mr. Schumer, when asked if he would support more financing for the Iraq war if the president requested the money, said he would.

“I have been rather hawkish. The bottom line is that I voted with the president on authorization to go into Iraq, I voted for the $87 billion to back up our soldiers, and I am never going to leave our soldiers out in the cold,” Mr. Schumer said. “I would support it. My regret for the president is not that he doesn’t have an aggressive foreign policy to fight the war on terror. He does. But he hasn’t executed it very well.”

On tax-cut policy, the three candidates took unsurprising positions. Mr. Schumer said he wants a middle-class tax cut, but he didn’t provide details.

Mr. Mills said he supported the Bush tax cuts. Dr. O’Grady called for more tax cuts to stimulate the New York economy.

Mr. Mills has been running against Mr. Schumer on the argument that New York would be better served by a moderate Republican if the Senate were to remain in Republican hands after November. Dr. O’Grady has said Mr. Mills doesn’t provide a real conservative alternative to Mr. Schumer, he’s too moderate, so she is running to provide one.

“Both my opponents speak of moderation and freedom, but they represent neither,” she said. “Both have tax-and-spend records in office. The truth is, they are both liberal and they don’t offer any clear choice in this race. I am running for office to offer a conservative alternative. We need to stimulate the economy by cutting taxes and creating jobs. I will work very hard to give us a better economy.”

Mr.Mills told voters in his concluding statement that he was leaving a safe seat in the legislature to give the people of New York a choice.

“Senator Schumer doesn’t want to answer questions on his record,” the Republican said. “He has introduced 163 bills and he has passed 12.We have lost money in every federal category. We’ve lost clout. We’ve lost influence. Mr. Schumer had a choice to make. He could be effective for the people of New York or be partisan. He was partisan.”

Mr. Schumer, with the luxury of a front-runner, focused on how much he loved his job.

“I am lucky,” he began. “I love going to work. I love the job as U.S. senator. I have worked very hard for the state and tried to make things better.”

Even if the debates manage to change the minds of some voters against Mr. Schumer, the senator has far more money than either of his opponents to woo voters back. According to the most recent filings, at the end of August, the incumbent had raised almost $25 million, compared to $531,000 for Mr. Mills and $47,000 for Dr. O’Grady.

Not participating in the televised debates were other candidates in the race, among them a wealthy developer and ex-convict, Abraham Hirschfeld, and the Green Party nominee, David McReynolds.