Mr Perot, who has been the party's candidate in the last two presidential elections, is facing a challenge to his control of the party from Jesse Ventura, the wrestler-turned-politician. Mr Ventura has made no secret of his view that Mr Perot, if nominated by the party to contest a third presidential election, will only lose the party votes. As one of his aides put it: "Perot got 19 per cent of the vote in 1992, and 9 per cent in 1996. If he ran again, he'd get 4 or 5 per cent. That is the wrong direction."
Mr Ventura's advantage is that in winning the governship of Minnesota last November against two establishment candidates, he showed he was capable of winning electoral office - something Mr Perot has never achieved. While Mr Ventura makes clear that he has no presidential ambitions himself, he is lobbying to get his favoured candidate elected party chairman. Russ Verney, the present chairman, a staunch Perotist, steps down on Sunday. Mr Ventura is backing Jack Gargan, a 68-year-old Floridian.
The decision on a presidential nominee will not be taken until next year, but the chairman will have a big say in the choice.
The suggestion that Donald Trump, the New York property developer, might seek the party's presidential nomination has been generally laughed off. However, another scenario, that of the party wooing Patrick Buchanan, the outside Republican Party candidate, is being taken more seriously, not least by the Republican Party, which could lose an electorally significant segment of votes if Buchanan was wooed away.