"The choices that I've made in my life are right for me," Mrs. Clinton told a panel of journalists, declining to discuss the details but saying they were rooted in her religious faith and "strong sense of family."
Mr. Lazio, trailing Mrs. Clinton in a new statewide poll, refused to touch the subject, saying he respected her private choices. The Republican candidate preferred to discuss his life-long residency in New York and eight years of experience in the U.S. House.
"The fact is that this race is about the issues, about who can be most effective for New York," the Long Island congressman said.
Mrs. Clinton's persona remains one of the major issues in the nation's most-anticipated Senate race, according to pollsters and voters. It is a race in which there are few neutrals, given voters' opinions of the first lady.
"She has a tremendous ability to stir emotions, pro and con," said Maurice Carroll, director of the Quinnipiac University Polling Institute. A Quinnipiac poll released Friday gave Mrs. Clinton a lead of 50 to 43 percent, with a margin of error of plus or minus 3.5 percentage points. That is the same lead Mrs. Clinton had in an earlier Quinnipiac poll, one conducted after the first Clinton-Lazio debate on Sept. 13.
Pollsters said voters criticized Mr. Lazio after that debate for walking over to Mrs. Clinton's side of the stage and demanding that she sign a written agreement to restrict campaign spending â€“ an incident the first lady cited at the start of their second encounter.
"Put your mind at ease," she told the Long Island congressman. "In case you've been worrying, I won't be coming to your podium today."
Mrs. Clinton later accused her Republican opponent of violating an agreement the two campaigns reached on campaign financing. It limited the use of soft money â€“ unregulated contributions that are spent by the political parties or outside groups rather than the candidates themselves.
"If New Yorkers can't trust him to keep his word for 10 days, how can they trust him for six years on issues like Social Security, Medicare, prescription drugs, and education?" Mrs. Clinton asked.
Mrs. Clinton referred to a Lazio television ad partially funded by the Republican National Committee. Mr. Lazio has pulled the television ad in question, but he denied any attempt to violate the agreement.
He then cited the number of Clinton contributors who have spent the night at 1600 Pennsylvania Ave., the address of the White House.
"Mrs. Clinton, please â€“ no lectures from Motel 1600 on campaign finance reform," Mr. Lazio said.
For the most part, the candidates refrained from attack during the hourlong session at a midtown television studio. The discussion ranged from regional transportation systems to Middle East violence to how a future Supreme Court might interpret abortion rights.
Mrs. Clinton again tried to link Mr. Lazio to former House Speaker Newt Gingrich and to the GOP's role in the 1995 government shutdown.
"Certainly, she's trying to make it an issue choice," said Lee Miringoff, director of the Marist Institute for Public Opinion. "He's trying to make it New Yorker vs. non-New Yorker, trust vs. no trust."
During the debate, Mr. Lazio said that Senate Republicans are unlikely to lose their majority, which currently numbers eight. Mr. Lazio said the state could use a member of the majority; the state's other senator, Charles Schumer, is a Democrat.
But Mr. Lazio must overcome a Democratic advantage in New York State, where analysts said party members outnumber Republicans by a 5-to-3 ratio. Pollsters estimate that the GOP Senate candidate will need at least 20 percent support from New Yorkers who plan to vote for Vice President Al Gore, a favorite to take the state in the presidential election.
The suburbs north of New York City are one place where Mr. Lazio might convert wavering Democrats, analysts said.
Mike Medonis, a golf course superintendent enjoying a weekend lunch in Larchmont, described himself as one of those Democrats, saying "I haven't signed off" on Mrs. Clinton.
"I've got the same issues everyone's got," he said. "Hillary not being from the state, her husband's being a jerk. But the economy's good. She's smart. I don't know much about Lazio."
Melvina Stohldrier, a retired bank teller from New Rochelle, said she is leaning toward Mrs. Clinton because of her hard work and her knowledge of state and local issues.
"I think she's going to help the schools and the kids," Ms. Stohldrier said.
At the end of Sunday's debate, Mrs. Clinton noted Mr. Lazio's attempts to make her the issue. She cited a Lazio fund-raising letter that told donors "all you need to know about this election are six words: I'm running against Hillary Rodham Clinton."
"Well, I think New Yorkers deserve more than that," the first lady said. "How 'bout seven words? How 'bout jobs? Education. Health. Social Security. Environment. Choice."
Mr. Lazio said New York voters can send a nationwide message that "it's people rather than government that we trust most ... and that if you don't stand up for something, you'll put up with anything."