Dr. Millin, the state Democratic chairman, said that getting a grip on Wyoming was probably a bit far-fetched, but that the party fully intended to capitalize on the excitement and to lasso into the fold as many new caucusgoers as possible. The state party has 18 national delegates to apportion  12 to be decided, directly or indirectly, by the caucus votes on Saturday, and 6 more, including 5 superdelegates, who could go to the August convention in Denver uncommitted.

“We’ll make the pitch on Saturday that politics and political races aren’t going to end today, and then invite people to help out other candidates,” said Dr. Millin, who supports Mr. Obama, of Illinois. “We’ll have lists of all the people who participate, and that should make a good starting point for the future.”

Image Republicans like Leroy Herdt counter that the supposed importance of the nominating contest is hype. Credit... Kevin Moloney for The New York Times

Of course, Democrats do get elected to office in Wyoming. A tradition of Democratic governors in particular extends back to statehood in 1890, with more years under Democrats  including the current governor, Dave Freudenthal  than under Republicans, according to Phil Roberts, a professor of history at the University of Wyoming.

And for about 70 years, until 1978, at least one member of the state’s delegation to Congress was a Democrat. (The Republican who broke the streak with his election to Congress that year, ushering in 30 years since of Republican supremacy? None other than Vice President Dick Cheney, who earned some of his first political chits here.)

Another historical quirk that could resonate here on Saturday is that one of the worst electoral droughts for Democrats in state history coincided with the years when Bill Clinton was president.

From 1994 to 2002, not a single statewide elected official or delegate to Congress was a Democrat. Dr. Roberts said that was partly a backlash to Democratic rule in Washington and partly because the party seemed to have written off Wyoming as a lost cause, a policy that he thinks has since changed.