AS Rudy Giuliani surges in the opinion polls for the 2008 Republican nomination, the children who once played supporting roles in his political life are nowhere to be seen.

Yesterday it was reported that the candidate’s relationship with his son Andrew, 21, and daughter Caroline, 17, had grown distant since his divorce from their mother, Donna Hanover.

Andrew admitted to The New York Times that he had difficulties relating to his father’s third wife, Judith Nathan.

Andrew, a member of the golf team at Duke University, said his determination to turn professional within three years would not leave him any time to take part in the Giuliani campaign.

“There’s obviously a little problem that exists between me and his wife,” he said. “And we’re trying to figure that out. But as of right now, it’s not working as well as we would like.”

Social conservatives have been wondering whether Giuliani’s “operatic” private life will withstand prolonged scrutiny. His first marriage to his cousin was annulled and his second to Hanover ended in a highly publicised divorce battle.

Revelations that Giuliani’s marriage to Nathan — with whom he had a public affair while mayor of New York — has strained relations with his children will heighten conservatives’ fears that his popularity may not last. The latest opinion polls show him with a lead of between 14 and 25 points over his nearest rival, John McCain.

Friends said that Andrew had been estranged from his father for at least a year. “For a while there, we weren’t talking,” Andrew said. “But lately we’ve been having more contact and trying to figure things out.”

Relations with Caroline, a high school student who is due to go to Harvard University next year, are also said to be difficult. Giuliani missed his son’s graduation in 2005 and has not attended his daughter’s school plays for 18 months, according to people who were present.

Nathan has her own share of problems, which will be difficult to keep under wraps. Shortly before the September 11 attacks of 2001 her ex-husband sought to gain custody of their daughter, then 16, alleging that the publicity surrounding Judith Nathan’s affair with Giuliani had disturbed the girl.

One Giuliani supporter described as “creepy” a recent photo-spread in Harper’s Bazaar of Nathan smooching with her husband and describing him as the “Energizer bunny”, the US version of the Duracell bunny in adverts for long-lasting batteries.

The family split emerged as Giuliani was wooing social conservatives in Washington. He told an overflowing hall at the Conservative Political Action Conference (CPAC): “You and I have a lot of common belief . . . We don’t all agree on everything. I don’t agree with myself on everything.”

Republicans do not regard Giuliani as their dream candidate, despite his heroic performance as “America’s mayor” during the 9/11 attacks.

He is pro-abortion, pro-gun control and lived for a while with a gay couple after splitting up with Hanover. But party activists have been warming to him on the basis that all the leading Republican candidates, as the family values campaigner Phyllis Schlafly put it, were “equally unacceptable” but Giuliani could be the most electable.

At the conference, Angela Poole, 22, from the swing state of Ohio, said: “I liked him a lot. He’s a little to the left of me on social issues, but you’ve got to balance that out with who can really win.”

Giuliani is racing to catch up with his closest rivals in terms of organisation and money. Republicans like to support the front-runner, but they have yet to be convinced that Giuliani will hold on to that status. Maintaining his lead is essential if he is to win the competition for money, known as the “invisible primary”.

Fred Siegel, Giuliani’s biographer, said the former mayor was beginning to rake in cash on Wall Street, but his organisation did not yet compare with McCain’s. “People are stunned by the early intensity of the campaign,” Siegel said. “The McCain people are hoping they will be the long-distance runners.”

Giuliani is certain to face further negative publicity for recommending that President George W Bush nominate the former New York police chief Bernard Kerik as homeland security secretary. It took only days for Kerik’s nomination to collapse amid allegations of sleaze.

“There will be a week on Judi Nathan, a week on Bernie Kerik and a week on the character of Rudy Giuliani,” said Siegel. “The question is how you navigate it.”

He is hoping to win over the Republican party base by bringing stalwart conservatives on to his team. The former solicitor general Theodore Olsen, who represented Bush against Al Gore in the Supreme Court election case in 2000, recently announced his backing.

But it was noticeable at the CPAC conference that Giuliani received a longer standing ovation before his speech than at the end. His delivery seemed unprepared compared to that of other contenders, including Mitt Romney, the former governor of Massachusetts.

Romney has been raising funds at an impressive rate, hauling in $6.5m in one day recently, but is struggling in the polls.

Jamie Johnson, 41, a conservative broadcaster and activist from Iowa, said: “The top three guys are all going to fizzle out. They jumped out of the gate too early.”

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