After cruising for months on stellar poll numbers and a steady flow of fundraising cash, Eliot Spitzer is facing increasing pressure to define more sharply his positions on issues ranging from property taxes, to school funding, to the death penalty.

While last night’s televised debate at Pace University between the Democratic candidates for governor, Mr. Spitzer and underdog Nassau County executive Thomas Suozzi, isn’t likely to send any major ripple through New York state politics, it put Mr. Spitzer’s proposed policies in the spotlight and forced the attorney general to take more concrete stances on issues that he has thus far tiptoed around.

In the first and only scheduled debate between the two candidates, Mr. Spitzer said he supported closing down the Indian Point nuclear power plants on the banks of the Hudson River, spending an additional $4 billion to $6 billion on school funding for New York City to satisfy a lawsuit that alleged that city students were being shortchanged, and that his support for the death penalty was qualified.

After the debate, Mr. Suozzi said his clashes with Mr. Spitzer provided a service for voters and demanded that the Spitzer campaign agree to more debates before the September 12 primary. “I’ll debate him any place, any time, and anywhere,” Mr. Suozzi said.

In rapid, staccato exchanges that were tense but for most part civil, each candidate tried to portray his opponent as incapable of governing a Byzantine state government with a budget of more than $115 billion. The debate was less about substance — few viewers probably came away from it with any serious knowledge about the candidates’ complicated tax-cutting plans — and about telling voters that his opponent is not what he seems to be.

Mr. Suozzi’s primary attack on Mr. Spitzer was that the attorney general was obsessed with Wall Street malfeasance during his two terms and ignored problems back home in Albany. He portrayed the attorney general as a candidate fearful of taking positions on issues so as not to offend the Democratic establishment that has embraced his candidacy.

“He has focused all his energy outside government,” Mr. Suozzi said. To that charge, Mr. Spitzer said, “I’m not trying to indict state government. I’m trying to take it over.”

Mr. Spitzer defended his credentials by alluding to his national reputation as a crusading attorney general. “I was called crusader of the year by Time magazine not because I am the voice of the status quo. I was called the best public servant in the nation by Reader’s Digest,” he said.

The debate rarely got personal, and while Mr. Spitzer vigorously attacked tax-cutting and school-funding plans proposed by Mr. Suozzi, he tried to stay above the fray. At one point, Mr. Suozzi asked him why the attorney general thinks Mr. Suozzi wouldn’t make a good governor. Mr. Spitzer took a pass.

In a surprise shot at the beginning of the one-hour debate, Mr. Spitzer tried to turn the tables around on Mr. Suozzi on the issue of taxes, saying Nassau County’s economic revival was a result of increases in property taxes approved by Mr. Suozzi. One of the most common attacks on Mr. Spitzer during the campaign from his opponents is that he would raise taxes.

“The reality is the financial turnaround is a consequence of one thing: property tax increases,”Mr. Spitzer said. Mr. Suozzi said he was the only county leader in New York who hasn’t raised property taxes “three years in a row.”

Mr. Spitzer, whose flashes of temper were the subject of news articles earlier in the year, portrayed Mr. Suozzi as the angry candidate. “You’ve compared me to all sorts of things,” Mr. Spitzer said. “You called me King George … and last time I checked, Tom, we hadn’t taxed any of your tea.”

The debate brought to light a number of differences between the candidates on contentious political issues. Mr. Suozzi said he was categorically opposed to the death penalty, while Mr. Spitzer’s stance was more complicated. The attorney general said he supported capital punishment for terrorists, people who commit crimes against humanity, or murder police officers.

After some forceful prodding by one of the questioners, Brian Lehrer of WNYC, Mr. Spitzer came out with a $4 billion to $6 billion range of additional operating money for city schools that he said would resolve the Campaign for Fiscal Equity lawsuit that has dragged on for years. Mr. Suozzi said $2.5 billion more in funding would do.

On a comic note, Mr. Spitzer said he wasn’t interested in running for president. Mr. Suozzi, to the amusement of the audience, said he was.

The most heated exchanges apparently took place back stage before the debate. Mr. Suozzi had brought a book with them that he had hoped to take to the lectern. Recounting what happened next in an interview with reporters after the debate, Mr. Suozzi said Mr. Spitzer exploded at him for breaking the set rules of the night. “Eliot Spitzer got really hostile and you’re not allowed to have a book… He started getting angrier, and angrier, and angrier.” Bob Hardt of NY1 News then took the book away and the debate proceeded. Mr. Hardt said Mr. Suozzi was told beforehand that he was forbidden to bring into the auditorium any visual aids and wouldn’t comment on whether Mr. Spitzer lost his temper. The three men were the only people in the room during the dispute over the book.