That is a question that more and more people will doubtless be asking in years to come. Mr Quayle was, when the girls had their brief and unenlightening conversation, a contender for the Republican Party's candidacy for the Presidency of the United States of America. By the time dawn broke this morning, the Iowa straw poll was set to ensure that he, along with probably one or two others, is virtually guaranteed to fail.
The straw poll is held every four years in the college town of Ames, just north of here. It is an informal sounding of how Iowans might vote next year in the Republican caucuses which help to select the candidate for the November 2000 election. It is also incredibly unrepresentative of the nation as a whole.
Iowa is a racially homogenous state descended mainly from German, British, Irish, Norwegian and Dutch immigrants. It is disproportionately rural and its inhabitants live in small towns (Des Moines, a rather dreary city of 200,000, is seen as a cross between 1930s Berlin and Calcutta). Its voters represent slightly more than 1 per cent of the US electorate. Only a small percentage vote in the caucuses - about 15,000 were expected to vote in the straw poll, which began as a party fund-raising exercise. Each voter has to contribute $25 (pounds 16), which is paid for them by the candidates. You do not even need to be a Republican. It is as if the population of a Lincolnshire village were pivotal in deciding the British government.
But the straw poll is vital. The media decided that it was a serious test after it alerted them to the strength of the fundamentalist Pat Robertson in 1987, and so a serious test it has become. George W Bush, the Governor of Texas, will almost certainly win, but the press will pore over his exact level of support to determine whether he did better or worse than expected. The second and third places will be crucial to ensuring survival beyond Ames. Mr Quayle was not expected to be among them.
And so there he was on Thursday, sitting beneath an E-Z-Up canopy at the Iowa State Fair, in between a root beer stall and a jewellery stand, being interviewed on Fox News. The former Vice-President looks sleek and successful, his hair now silvered, a small bald patch at his crown starting to spread. But he also looked a little bleak. The interview finished, he stood and gamely plunged into the crowd to shake hands and share pleasantries with the good people of Iowa. Somewhere in the back of his mind he must have known that these were likely to be among his last days in politics, that a long road would end in a small college town in Iowa.
The good side of Iowa is that it forces everybody, high or low, into what Americans call retail politics: meeting and greeting voters individually. Iowa's party organisation is about small groups working together and, to win, a candidate needs Bolshevik organisation, a plausible manner and the ability to show ceaseless interest in pigs. At the state fair, the candidates are judged by standards similar to those applied to the hogs that are paraded in the Swine Barn.
Mr Quayle was once an important man: the Senator from Indiana, and then Vice-President of the United States. We remember him as the one who couldn't spell "potato", but he is actually a bright man who attracts a lot of conservative voters, and George Bush chose him as his running mate in 1988. Once, he had Secret Servicemen to protect him, a large house on Observatory Circle above the British embassy in Washington, and a Marine helicopter to ferry him across town so that his neighbours would look up every time they heard the juddering machine and think: there goes power. And here he was shaking hands by JR Do-Nuts in Des Moines, trying to persuade individuals to make the 30-minute drive to Ames to cast their votes so that his job would go on.
It does not do to be too folksy about this, of course, as Mr Quayle has pointed out. Mr Bush is succeeding because he has money. Mr Quayle would, if the campaign finance figures are to be believed, have trouble getting together the small change to buy a root beer. Mr Bush could get every man, woman and child in the state a Jumbo Bag from JR, and have change left to buy them a Chocolate Frosty Malt. (Perhaps that is why they call it retail politics.) But Mr Bush is also a polished public performer: were there ribbons given for grip 'n' grin in the Pioneer Pavilion, he would be a winner.
Mr Quayle is said to be irritated, feeling that this is his turn: he did not spend all those year as Vice-President, being lampooned by the Washington press and attending state funerals in Latin America just for the helicopter rides; he always believed that he would be President, and that this would be his year, and here come the Bushes ruining his show.
But then US politics is not fair. Fortune does not always smile on hard work and virtue, and, even if it did, Mr Quayle would probably get little more than a quick smirk. It is a thankless business, being Vice-President.
On the other side of the State Fair Ground was another man who knows this all too well: Al Gore, the most likely Democratic candidate and Mr Clinton's Vice-President. Mr Gore has lived in Observatory Circle since 1993 and is well known and reasonably well respected, but he is regarded by the press and many voters as stiff and a little dorky. He has worked very hard, but that will count for little in the year to come. It is all about retail politics from here, and the money that funds it.