Mr Giuliani had heard the question many times before, as has every mayoral candidate across America in a year which is seeing the largest turnover of big city mayors in three decades. Violent crime is the big issue and he had always promised a crackdown. But in the synagogue he had to tread carefully. These people were mostly Democrats; law and order was not traditionally their first priority. Taking care to be politically correct, Mr Giuliani said he couldn't clean up the city for one man, or one neighbourhood. He intended to clean it up for everyone, all the nine million people in all five boroughs of New York City.
The audience of several hundred applauded. Mr Giuliani's wooden face broke into a thin-lipped half smile, which is about as emotional as the former US prosecutor gets, but this was a special occasion. He was taking his campaign against Mayor David Dinkins, the city's first black leader, right into the heart of the swing voters who will make the difference on 2 November.
With other ethnic groups pretty much spoken for, the white Jewish liberals will either do what they did last time in 1989, which was to give Mr Dinkins a tiny victory of two percentage points, or they will put Mr Giuliani in the mayoral mansion. Judging by the enthusiastic response to Mr Giuliani's law and order programme, Mayor Dinkins could lose. Such is the overweening feeling of a city in decline, and of the mayor's failure to bring jobs and refurbish predominantly poor neighbourhoods, that people are willing to give someone else a chance.
There is also another less obvious and mostly unstated reason for the mayor's probable defeat. In 1989, many liberals voted for Mr Dinkins because it was the politically correct thing to do. But there is strong evidence that the political correctness of liberal reformers has now become establishment orthodoxy and is on the wane. Those liberals who voted for Mr Dinkins because he was the first black with a chance of victory do not have the same pressure on them this time. Many appear to feel they can vote against him.
Mr Giuliani, a man whom George Bush once called America's crime fighter, has pulled all the right strings for a middle-class community fed up with violent crime, streets of beggars, homeless people urinating in doorways, and, of course, drug addicts. Mr Giuliani's audiences rarely flinch when he says he is going to lock up the petty drug pushers - something which the Dinkins people purposely avoided in favour of going for the so-called 'king-pins'. When Mr Giuliani says he is going to fine people who litter the streets and that those who can't pay will be sentenced to community service, his listeners could not be more enthusiastic. They applaud his pledge to lower parking fines and put an end to blaring 'boom boxes' and the residential drag racer. And when he says he is going to bring back the legal statute definition of assault, which says that anyone who makes you feel afraid of imminent bodily harm, or even just plain nervous, has committed assault, they nod unquestioning approval. After all, there's hardly a New Yorker who hasn't feared an attack at some time. For the record, Mr Giuliani is also against parole and for the death penalty.
This is a lot to stomach for a traditionally Democratic electorate that has favoured liberal sentencing policies, been against the death penalty and in favour of parole. But New Yorkers have never been so fed up with their declining living standards and their constant battle with crime. Even in the Sixties, when heroin addicts roamed the streets accosting passers-by for dollars 5 for a shot, and in the Seventies, when crack cocaine became the new and more dangerous drug of choice, there were never such signs of prolonged and obvious decline in the quality of life. In the Sixties, liberals were too busy seeking social change and enjoying their own newfound permissiveness to complain about the emerging criminal class. In any case, in those days and later, in the Seventies, the abiding philosophy was that the poor and the drug addicts could be dealt with on welfare rolls and by community drug programmes. In the Eighties, the middle class made too much money to care about any social issue very much - until their own bubble burst.
Those who had bought New York real estate at the top of the market, at the end of the Eighties, found they couldn't sell when their taxes went up; the schools became too violent; the beggars got more numerous and people wanted to escape to the suburbs. They were stuck.
The synagogue audience applauded again and again as Mr Giuliani said he would reduce their taxes, and those of hotels and businesses, in order to bring back 400,000 lost jobs. He would reduce the city government to help pay for it all. In short, like Bill Clinton, he would 'reinvent' government. It was the only way, he said, to stem the flow of the middle class - the city's tax base - to the suburbs and also to prevent New York's nightmare: a city of the very rich and the very poor. Maybe he could be a miracle worker.
How genuine the applause really is will be known in two weeks' time. The polls put the two candidates neck and neck, with neither Mr Dinkins nor Mr Giuliani commanding any great confidence in their ability to make the changes each says he will carry out to improve life.
With much justification, New Yorkers have become totally cynical about the claims of their leading politicians to have miracle cures. In recent memory they chose the conservative Democrat bachelor Ed Koch for 12 years, but he did little more than fulfil their quirky desire to have an eccentric loudmouth selling New York to the world. In the end, he was a brash, divisive leader who pitted ethnic and religious groups against each other. David Dinkins, an outwardly civil but exceedingly dull, long-serving member of the city council, was voted in as the great conciliator, a man who was going to create a 'gorgeous mosaic' out of all the races and religions. It didn't happen.
'Have a nice day' has given way to T-shirts saying 'Back off', or worse. There have been particular moments of nastiness from characters like Howard Stern, the shock radio disc jockey. He has just published his autobiography to frenzied acclaim, especially in New York. One of his choice thoughts on Rodney King, the police victim of Los Angeles: 'They didn't beat this idiot enough.'
Mr Dinkins presided over race riots, the worst being the clash between Jews and blacks in the Crown Heights section of Brooklyn. The riots started after two black children were run over by a car driven by a Hassidic Jew. In retaliation, a mob of black youths knifed a Hassidic student to death. The official report blamed the mayor for a lack of leadership in not bringing the riots under control sooner.
The kind of remark you hear repeated by middle-class liberals these days goes likes this: 'I am a lifelong Democrat and I feel terrible about deserting David Dinkins. I voted for him largely because he's black. But now I'm voting for Giuliani.'