His rise has defied many of what are regarded as the iron rules of campaigning. It has not been propelled by vastly successful fund-raising, or expensive campaign advertising, or by an elaborate party machine.
Instead, Mr McCain has advanced largely by personal grass-roots campaigning and a well-timed and well-received book. He also has the public mood to thank, a mood looking beyond President Bill Clinton with a combination of fondness for his most attractive traits, and disgust towards his worst.
If surveys are to be believed, voters next year will be less concerned about policies than character and integrity. This has not prevented the favourites on either side, Mr Bush and Vice-President Al Gore, from pronouncing in extensive detail on policies.
But Mr McCain, in common with the Democratic challenger, Bill Bradley, is campaigning as much on character and on his singular life-story. And, like Mr Bradley, he is enjoying a surge in New Hampshire that could spread beyond the north-east.
In the Senate, Mr McCain, 63, is known as a feisty and principled fighter. He has been in the forefront of efforts to reform campaign financing and made it clear that he would not vote to convict Mr Clinton in last year's impeachment trial.
It is less Mr McCain's Senate record that has caught the public imagination than his war record. The scion of a military family, he is the son and grandson of admirals. He graduated from the Annapolis naval academy, qualified as a pilot, and volunteered for Vietnam.
At school, at the academy and in his early postings, Mr McCain was more than a bit of a lad. He pushed the rules as far as they could be pushed without failing; he took his punishment like a man, but was fundamentally unamenable to discipline, and barely graduated. Drink and girls were his particular weaknesses, but - at least so far as can be gleaned from friends and his autobiography - he was always honourable and never malicious. He was also brave, surviving a crash during training and a fire on the aircraft carrier Forrestal in 1967.
All this stood him in good stead in the most testing time of his life. Within a month of starting his pilot's assignment he was shot down over Hanoi. Severely injured, he withstood physical deprivation, ill-treatment and torture. Eventually broken into signing a (limited and grudging) confession, he made half-hearted attempts at suicide but refused early release to uphold the military code of honour and not to compromise his father, then admiral in command of the Pacific theatre. He was released in 1973 and left the service, a captain, in 1981.
He tried to put Vietnam behind him when he embarked on politics. But for voters it is testimony to his character and fitness for office. His knowledge of the world, self-deprecating manner, and even the fierce temper his political enemies have tried to use against him in recent weeks, are all seen as recommendations. Some of his recent surge he owes to the withdrawal of other candidates, most recently Elizabeth Dole. But that is not the only reason.
Underpinning his support is the courage and dignity he displayed in a war that still divides the United States. That may not win him the presidency, but in an America hungry for heroes, it could take him a very long way.