A minute earlier, in another part of the maze, the imperial caravan of the President sweeps by, taking, it seems, 10 minutes to pass, flattening bystanders against the corridor walls. Barbara Bush strides ahead, the President wanders uncertainly behind, surrounded by a score of officials and dozens of agents with spiral wires coming out of their ears.
Here is the appeal of Perot: the little man ready to challenge the cumbersome, quasi-corrupt structure of government; the amateur, walking alone through the maze of politics, who shows up the over-sophisticated professionals. This is one of the most endearing self-myths of the United States, or at least of the Hollywood version of the US, best expressed in Frank Capra's movies.
Unfortunately for Mr Perot, the week did not quite follow the script. After satirising the 'alligator shoes' of the US political establishment in the first debate, Mr Perot made a fool of himself in the second. Faced, for the first time this year, with an audience of real, uncommitted voters asking real questions, he was left to babble about 'hundreds of plans all over Washington'. To implement the best of them - whichever they might be - he would 'get everybody holding hands'.
It was Governor Bill Clinton, often derided (sometimes fairly) as a slick, robot-candidate, who formed an instant relationship with the 209 members of the studio audience. In the artificial, triple press conference of the first debate, Mr Clinton was competent but artificial; in the intimate atmosphere of the second, he was competent and intimate.
Why? Because in this year of anti-politics, politics will out, and Mr Clinton is one of the most uncontrollably natural politicians around. The Richmond audience demanded ideas and facts on serious issues: the economy, education, health care. It angrily forbade the candidates to speak of draft-dodging, or Iran-Contra, or Saddamgate or bimbos.
Into the vacuum flowed the traditional, and undeniably slick, skills of the politician: issues studied and factoids remembered and presented in coherent, finished sentences. Some of the audience felt afterwards that Mr Clinton had hosed them with pre-digested information and two solutions for every problem. Many others were charmed. He stayed in the arena chatting and signing autographs for 30 minutes after the other candidates had left. Despite all the bizarre events of the 1992 campaign, a new seriousness has overwhelmed US politics. Several pundits have already pronounced the real heroes of the campaign to be the American voters, who have refused to be distracted by mud or balloons, and have focused rather single-mindedly on themselves.
More than 80 million Americans watched the first debate, about 90 million the second: 20 per cent more than in 1988. Nearly two thirds of all TV watching households tuned in on Thursday. In answer to pollsters' questions, 80 per cent of registered voters say they are giving 'some' or 'quite a lot of' thought to the election, the highest level of interest since the 'Vietnam' election of 1968.
It is traditional for Europeans to mock the sophistication of American voters. It is only four years since the same electorate swallowed George Bush's visits to flag factories, and only eight years since it swallowed Ronald Reagan's vacuous Morning Again in America campaign. This is the same electorate which helped to create the Washington gridlock it now abhors, by voting for Republican presidents and Democratic Congresses throughout most of the past 24 years.
What has changed? First, Americans have become more than usually cynical about politicians (the Savings and Loans mess, the Anita Hill-Clarence Thomas hearings, the deficit, the Congressional banking scandal). As a result, voters are innoculated against the crassest kind of political nonsense.
Second, the economic stagnation of the early 1990s has made voters anxious about their jobs, mortgages, health care and their children's future. The electorate wants the election to be about its own problems, not the politicians' peccadilloes.
The Richmond audience asked not about crime, race, welfare or even taxes, but: 'Why can't your discussions and proposals reflect the genuine complexity of the issues?' And: 'What are your plans to improve the physical infrastructure of this nation?'
Throughout the year, the electorate has refused to allow its anger to be hijacked for dubious causes. Few Republicans ran with the quasi-fascism of Pat Buchanan or David Duke. Few Democrats were tempted, in the end, by the anti-establishment fundamentalism of Jerry Brown. The electorate rejected - actually resented - the Bush campaign's attempts to make an issue of 'family values', the Godlessness of Democrats, or the Vietnam draft status of Bill Clinton. The electorate twice flirted with, but quickly saw through, the chuck- wagon wisdom of Ross Perot.
Slick though he is, as capable of mud-slinging as he was in the Primaries, as fudged as his budgetary figures are, Bill Clinton is the candidate who has found the right package for the times: addressing Americans in a half-way adult manner on the issues that worry them.
Leaving the debate at the University of Richmond, one of the many people trying to recall where they had parked their cars was Uncle Sam himself, in full stars-and-stripes suit and top hat. Uncle Sam Rounseville, 53, is a retired textile executive from Massachusetts, who changed his name from Leroy Lincoln Rounseville last year. He now spends his savings travelling the country dressed in red, white and blue, with a sign that reads: 'Vote on 3 November or don't blame me.'
'Sure, the politicians are to blame but how can you complain if you didn't vote?' he said. 'How can you complain if you don't study the problems and listen to the arguments?' Uncle Sam also detects a new single-mindedness and seriousness among US voters. He predicts a record turnout two weeks on Tuesday (a modest rise is more likely).
Voter high-mindedess will be given its final, and perhaps only true, test in the next fortnight. The Bush campaign is heading into scorched-earth mode, starting probably with the final debate tomorrow. Expect new plagues of draft-dodging allegations, tax- raising allegations, perhaps even bimbo allegations.
Democratic strategists say tax- and-spend is the only issue that may penetrate the self-absorption of the electorate. Two misleading television ads, accusing Mr Clinton of planning stealthy tax rises, are already having some effect in key states. But the serious, even pompous, mood of the Richmond audience, drawn from one of the most conservative cities in the nation, suggests that much of the Republicans' boiling oil may fall on their own man.