Ashcroft never made it past the second round of balloting for the chairman's job, which said something revealing about internal party contests.
In some respects, they are more like student council elections. Since only the 168 members of the national committee get to vote, personal popularity and connections can be extremely important. Those without strong ties to the national committee - Newt Gingrich may come closest to fitting that profile this time, if he decides to compete - are often at a disadvantage.
The runner-up in 1992 was Spencer Abraham, a former chairman of the Michigan Republican Party (a state party chairman, a job Steele once held, is an automatic member of the national committee). Abraham, like Ashcroft, would go on to win a single Senate term two years later and land a Bush Cabinet slot as a consolation prize after getting voted out in 2000.
The winner that year was Haley Barbour, a lawyer, lobbyist and party insider who, as The New York Times said in reporting his selection, was "not well known nationally."
He is now. He's in his second term as governor of Mississippi and sometimes talked about as a potential candidate on a future national ticket.
Most of those angling to be the next chairman have RNC ties, including at least four current or former state chairmen and the current top dog, Mike Duncan, who may want another term.
Duncan's may not be a familiar name in your household, but it is in the homes of RNC members, whose many needs, such as good hotel rooms at the national convention, the Republican chairman has carefully tended over the past two years.
Bill Brock says none of the current aspirants for his old job have been in touch to seek his advice. That may be a mistake.
Brock says it's time for Republicans to stop criticizing each other and start living up to the party's principles. He believes Republicans need a grass-roots revival and fresh outreach to communities that think they have no voice in the party, including women, minorities and blue-collar workers.
As he points out, there's no way to get to a majority on the votes of middle- and upper-income whites only.
Republicans "have got to start listening, instead of talking," Brock says.
Steele, in laying out the principles of his latest campaign, makes some of the same points.
"Most Americans today see a Republican Party that defines itself by what it is against rather than what it is for. ... We exclude far better than we welcome," he wrote in The Wall Street Journal. "We have to listen to what Americans are telling us about their hopes, desires and needs, and then translate that message into proposals for meaningful action squarely grounded on the values we Republicans have always stood for."