But the consensus is that whatever the impact of his 11th-hour candidacy is in individual states, he is unlikely, as matters stand, greatly to interfere with Bill Clinton's apparently predestined glide to victory on 3 November.
Mr Perot's news conference in Dallas was a vintage effort, combining all the features which earlier this summer enthralled a nation, but now irritate it: the imperious conviction that he embodies America's will, a bristling dislike of the press, and the tirelessly restated belief that neither Republicans nor Democrats are addressing the problems of debt and industrial decline.
No one can be certain of the campaign he will wage before polling day, except for two things: there will be precious little contact with the journalists whose investigation of his career prompted his first withdrawal last July, and that - as when he once rode so high in the polls - television will be its centrepiece.
'Would you expect me to reveal my strategy?' he said on Thursday. In fact, an advertising avalanche is ready to be unleashed on the small screen, while rumours abound that he is booking half- hour network slots from next week, for the 'town hall' question-and-answer shows with the public at which he excels.
Alas the public is no longer so enchanted. Perot, the would-be messiah, is now just Perot the spoiler. According to the daily political newsletter Hotline, he will not alter the outcome in a single state. A poll in yesterday's Los Angeles Times suggests that even in California he trails Mr Clinton by 32 points and Mr Bush by 11. Nearly two Americans in three believe he should have stayed out.
But for the Bush camp these days, anything that shakes up the contest is good news. Although Mr Perot could damage the President in the battle for the big Southern prizes of Florida and Texas, the White House clings to the hope that even modest Perot inroads could tilt key Rust Belt states like Ohio and Michigan its way. Then there are the debates.
Negotiations between Bush and Clinton advisers this week have at last yielded a compromise: there will be three presidential debates and one vice-presidential match- up, crammed into a nine-day period between 11 and 19 October. The formats will vary, accommodating the wishes of the two sides. Most tantalising of all, if both sides are sincere, Mr Perot will be taking part.
There, if anywhere, lies the chance to confound his critics, bring his radical deficit-cutting proposals to the forefront of the campaign and alter its dynamic. In a contest whose hallmark is not so much affection for Mr Clinton as disaffection for the President, a three-way confrontation could upset every calculation.
But Mr Perot's road remains steeply uphill. Every precedent is that independent candidacies fade as election day approaches. Moreover, his vow to 'stick to the real issues' is a formula that works in business, but not in the cruel arena of politics, above all one where the press is unremittingly hostile, if not openly scornful.
Strident, pugnacious and self-righteous, Mr Perot's personality will be under the microscope again. And the experience could be miserable. 'I don't think there is anything about the rest of this that is going to make him anything but unhappy,' his long time associate Thomas Barr told the New York Times yesterday. 'It's going to be more of the same that he hated before.'