This Saturday's Wyoming county Democratic conventions are fast becoming something this state rarely sees - a political battle with national implications.
A month ago, the fight that Colorado Sen. Gary Hart picked here with Walter F. Mondale appeared important only to the Hart campaign. Senator Hart's unexpected successes in New England changed that.
As the last test before Super Tuesday on March 13, overwhelmingly Republican Wyoming has gained an importance that far exceeds the clout of its 15 delegates to the Democratic National Convention.
Hart strategists originally saw Wyoming as a last chance to win a state and keep his campaign alive going into Super Tuesday. Capping what could be a four-state winning streak with a decisive victory in the first Western contest is a new goal.
Mr. Mondale's supporters, who two weeks ago predicted the former vice-president would prevail in Wyoming, now say they hope to slow Hart's momentum by staying close in the Coloradan's own backyard.
''If we come close or beat them, it's a real significant loss,'' says Tom Cosgrove, Mondale's Wyoming field director. ''The only way they can win is to blow us out of the water.''
Hart did just that in a Casper Star-Tribune poll of county Democratic officials. The newspaper spoke with 112 of 134 such officials. Of the 85 who backed a candidate, 64 favored Hart, 18 prefered Mondale, and two declined to comment. Three respondents backed other candidates. Twenty-five remained uncommitted.
Many of those backing Hart said they felt he had the best chance of unseating President Reagan. Hart's perceived independence of special interest groups was also cited.
Mr. Cosgrove attributed Hart's strength among party activists to the efforts of Cheyenne lawyer Rodger McDaniel. Hart campaigned on Mr. McDaniel's behalf during an unsuccessful 1982 bid to unseat Republican Sen. Malcolm Wallop.
Cosgrave says he doesn't find the poll's outcome surprising. ''There is a new guard coming on in the party, which is very closely associated with Rodger McDaniel. It is not reflective of all Democrats,'' he says.
He says he hopes to counteract Hart's support among party activists by attracting Democrats who ''are not traditional conventiongoers.'' The Mondale campaign has brought 12 full-time workers into the state to make that effort.
But Cosgrove concedes it will be an uphill battle. He says Hart has built an advantage by organizing sooner and better, by television advertising, and by being the only candidate to visit the state.
''Despite all that, I think we'll be competitive,'' Cosgrove says. ''Hart has to win by a large margin to call it a victory. I hope to cut into that margin.''
The strategy for doing so does not include an advertising blitz or bringing Mondale to Wyoming. Cosgrove said he sees Hart's heavy spending in the state and consideration of a fifth visit as signs the senator is growing concerned.
Not so, Hart campaign coordinator Trevor Cornwell says.
''We're not terrified,'' he says. ''We're working hard, but we're not shaking in our boots.''
If Hart visits the state before Saturday, it will be because he had plans to do so earlier, Mr. Cornwell says. It is more likely that Hart will opt to campaign in the three Southern states that hold primaries on Super Tuesday, he says.
Hart has already devoted considerable time to Wyoming, visiting Casper, Cheyenne, and Laramie in recent months. Last summer, he spoke at an anti-MX rally in Cheyenne.
Those visits account for much of Hart's advantage. Wyoming has fewer than 500 ,000 residents, and political campainging here is very much a one-on-one activity.
Hart supporters have used Mondale's failure to participate at the one-on-one level to substantiate their claim that the former vice-president does not care about the West.
The Hart effort has relied heavily on local organizers, Cornwell says. They have focused their efforts on Democrats who are most likely to attend the county conventions. Cornwell says Hart's strong showing in the Star-Tribune poll indicate his strategy has worked.
Among those supporting Hart were several original members of Mondale's state steering committee and a former organizer for Sen. John Glenn. Hart has also received the support of Sen. Alan Cranston's state campaign director.
Although Cornwell says the poll may overestimate Hart's strength, he says he is confident that Wyoming in Wyoming will give Hart a final boost before Super Tuesday.
''We need to continue momentum,'' he says. ''Indications are we will be able to do that in Wyoming.''
Delegates chosen at the county conventions Saturday will select Wyoming's 15 representatives at the May 5 state conclave. The county meetings are opened to all registered Democrats.