At least 10 per cent of the city's 3 million registered voters are still wavering, according to the polls. These perplexed people have been changing their minds from day to day, and many say they will not finally decide until they pull the levers in the voting booths.
In other US elections with a large number of undecided voters the challengers have been winning, suggesting that Mr Giuliani will be the victor and reverse his narrow defeat at the hands of Mr Dinkins in the 1989 election. In addition, much as the two candidates have said race does not matter, the record elsewhere shows that when a black Democrat has been challenged by a white Republican and the wavering voters are mostly white Democrats and independents, as is the case in New York, the white Republican candidate has won.
It is little wonder New Yorkers have had trouble making up their minds in this bitter contest. The two candidates inspire no great loyalty and have engaged in round after round of childish tit-for-tat. Despite pressing issues of crime, jobs and schools, the bickering has been at such a low level that New York Newsday put the two men in pale blue swaddling clothes on its front page, under the banner headline 'Two Big Babes'. Then the paper ran a regular column of the candidates' baby-talk.
Typical items: 'Mr Mayor why won't you debate Mr Giuliani on televison?' Mr Dinkins: 'Why should I?'
'Mr Giuliani, Mr Dinkins says that 12 years of Republican rule in the White House caused the loss of jobs in New York, what do you say to that?'
Mr Giuliani: 'The mayor probably thinks that Ronald Reagan is still President.'
In the campaign, Mr Dinkins has tried to overcome the widespread impression that he is an incompetent manager, and Mr Giuliani, a former federal prosecutor, has striven to persuade the voters that he is not the cold, heartless conservative the mayor says he is.
The election seems to be in the hands of about 300,000 Jewish, Hispanic and white liberal voters who make up the undecided block. They are the ones who put the mayor in office last time, and they could kick him out today.
If the 66-year-old Mr Dinkins loses, it will not be for lack of support from his party. Bill and Hillary Clinton have been here twice. The Rev Jesse Jackson has been a permanent fixture for the last week, Barbra Streisand has been embracing him in front of the television cameras and several Democratic congressmen have joined the mayor on the campaign trail.
In a city whose voters are registered as 70 per cent Democratic, 14 per cent Republican and 14 per cent Independent, Mr Giuliani, 49, has battled for the crossover voters by pledging to include leading Democrats in his administration should he be elected. In the final hours he was urging voters to have the courage to cross party lines and 'work together to save our city'.
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