And sure enough, when they emerged to board their planes, our two heroes threw off their jackets and made a beeline for that football. Seconds later they were bounding around throwing ferocious passes, a couple of regular jocks. No matter that we were already half an hour behind schedule. Rule one of a candidate's life is that punctuality comes a distant second to Godliness. And Godliness, as far as Campaign '92 is concerned, means looking virile and getting your photo taken.
What is it about US presidential elections that brings out the sportsman? Not that it took much bringing out in the case of George Bush. His entire term of office has been one endless athletic proving ground, from horseshoes to golf to jogging to baseball to - most recently - the un-American activity of soccer. Maybe the prospect of the 1994 World Cup on US soil beckons, maybe it was the cruder matter of the Hispanic vote. There, spread across Sunday's papers, was the 41st President in a minutely choreographed kick- around with the six- and seven- year-olds of the Plaza Grill team in Montgomery, Alabama.
But you expect this sort of thing from Mr Bush. Less easily explained are Bill Clinton's tendencies in the same direction.
To put it politely, based on what I've seen so far, he is not one of nature's games-players. Mr Clinton on the run is a grisly spectacle, less a jog than a leaden plod. But every morning on the campaign trail, 'The Jog' is the first item on the agenda for pool coverage. Not only must it be done (the candidate tends to be overweight); it must be seen to be done. The same goes for Mr Clinton lumbering round the bases on the softball diamond, another occasional campaign event. Judging by what I witnessed at Midway Airport, he is marginally happier with a football in his hands. The question remains, why do they do it?
The answer, surely, lies deep in the American psyche. Part of it is the dreaded 'wimp factor'. Whatever else, a US politician here must never appear a wimp - just ask Mr Bush, who spent most of the 1980s trying to throw off that label. Perceived wimpishness has destroyed many a presidential contender: from Ed Muskie who ruined his chances in 1972 by weeping in public at a letter attacking his wife, to Michael Dukakis in 1988.
Another cardinal rule is never, never, betray a fondness for the cerebral side of life. Intellectualism is first cousin of wimpishness and the related sin of womanliness (which may explain it is so difficult for a woman to run for president). Take Adlai Stevenson, who in the 1950s earned the deadly epithet of 'egghead' in his two losing contests against Dwight Eisenhower. The New York Daily News had a field day, berating 'Adelaide' and his friendliness with 'lace-panty diplomats'.
Thus, Mr Bush's attacks on Mr Clinton and his fellow 'social engineers from Oxford' honour a long tradition. And that explains why Mr Clinton, arguably the most expert and intellectually prepared of any recent candidate for the White House, would rather be seen dead right now than with a book.
But, you may argue, there is still more to it. Starting with George Washington, is not the battle for the presidency a re-enactment of that quintessential American drama of the ordinary guy who becomes a hero by taking on and vanquishing the system? Thus the symbolism of the debates, as ritualised single combat and test of spiritual manliness. Note, too, that the campaign trail sports are those of Everyman: baseball, football, basketball - but certainly not golf. Golf is Mr Bush's favourite - but far too elitist for the campaign trail. The liberator of Kuwait could be seen striding the fairways of Kennebunkport, but not an underdog fighting to hang on to the White House.
Which leaves Ross Perot. He doesn't jog or throw footballs (at least not in public); indeed he scarcely campaigns at all. But in other respects he fits this theory perfectly, the living myth of the little man who took on Vietnam, General Motors, and most lately the established order of Washington. The recipe was perfect. A pity he sees conspiracy at every turn. If not, he might have won.