Republican Rudy Giuliani said Thursday that people should "leave my family alone" when asked by a New Hampshire woman why the presidential candidate should expect loyalty from voters when he doesn't get it from his children.

Giuliani has a daughter who has indicated support for Democrat Barack Obama and a son who said he didn't speak to his father for some time. His ugly divorce from their mother, Donna Hanover, was waged publicly while Giuliani was mayor of New York. Giuliani has since remarried.

Answering questions at a town-hall meeting, Giuliani was asked why he should expect loyalty from GOP voters when his children aren't backing him.

"I love my family very, very much and will do anything for them. There are complexities in every family in America," Giuliani said calmly and quietly. "The best thing I can say is kind of, 'Leave my family alone, just like I'll leave your family alone."'

His comments were greeted with a smattering of applause from the audience of about 120 people. Giuliani urged them to judge him based on his performance as mayor and a federal prosecutor, and he launched into a list of his successes such as reducing crime and welfare and prosecuting organized crime figures and drug dealers.

The questioner, Derry mother Katherine Prudhomme-O'Brien, opened by thanking Giuliani for how he handled the Sept. 11, 2001, terrorist attacks and introduced him to her 5-year-old daughter, Abby, who was playing on the floor next to the platform where Giuliani stood.

Prudhomme-O'Brien, 36, wasn't certain about Giuliani's answer.

"If a person is running for president, I would assume their children would be behind them." she said. "If they're not, you've got to wonder."

She said the issue is a question mark that is "going to stay there for a lot of people."

Giuliani mentioned his wife, Judith, when he answered a question about Alzheimer's disease, saying she had helped raise money to fight the disease.

"We've been touched by it very close to our family, too," he said.

Giuliani focused on health care during the hour-long forum, saying that buying health insurance ought to be like buying insurance for cars or a home, with people buying their own policies with different deductibles and types of coverage.

Employers and the government "never buy precisely what you want: they buy what they think is generally good," he said.

Giuliani wants to give families a $15,000 tax credit to buy insurance privately rather than through employers, and he proposes that any money left from the credit be kept in tax-free health savings accounts.

In South Carolina, Giuliani launched a new radio ad focusing on illegal immigration and his record as mayor. The spot outlines Giuliani's plan to deport illegal aliens who commit crimes, bolster border protection, and it reiterates his belief that newcomers to the U.S. should learn English. He is running a second spot highlighting his work as mayor on cutting crime, trimming welfare rolls and reducing taxes.

Giuliani answered several questions about immigration on his swing through New Hampshire Thursday, as a video circulated of him taking a seemingly softer line on the issue in 1996.

"We're never, ever going to be able to totally control immigration in a country that is as large as ours," he said in a 1996 address to Harvard's John F. Kennedy School of Government. "If you were to totally control immigration into the United States, you might very well destroy the economy of the United States, because you'd have to inspect everything and everyone in every way possible."

On Thursday, Giuliani told reporters the statement is not inconsistent with his views today that he wants to end illegal immigration and expand legal immigration.

"Back in 1994 and 1995, we didn't have the technology" for controlling illegal entry into the United States, he said.

"The only way you can cover the border is with a high-tech fence," he said. "We are now at the stage where we can do that. We've probably been there for the the last three or four years."

Giuliani has spent the week visiting three early voting states — South Carolina, Iowa and New Hampshire — after focusing for several weeks on California and other delegate-rich states that will vote later, most on Feb. 5. He said his campaign has solidified his position in the larger states and is now stepping up efforts in the earliest states.

"We have our biggest organizations now in Iowa and New Hampshire; we're going to spend a lot more time here," he said.