With one exception, Utah's most influential Democrats have thrown their support behind a Michigan campaigner in the fight to determine the national party's future.

Three of the four Utahns empowered to vote for the party's new national chairman next month say they will vote for Rick Wiener, an attorney who served six years as his state's party leader, officials said Friday.Wiener, who appeared at an afternoon news conference at the Utah Capitol, said he has two-thirds of the 195 votes he needs to win the election Feb. 10.

His chief competition is Washington lawyer and lobbyist Ron Brown, who met with news reporters and executives in Salt Lake City on Friday. Brown, convention manager for Jesse Jackson's 1988 presidential campaign, has the support of former state chairman Pat Shea.

Brown contends he has the deep support of a broad range of interests within the party. The current member of the party's Executive Committee referred to the support Wiener has as "10 miles wide and 1 inch deep."

"I think one of the things the party is going to have to do is unify," he said. "I have not only talked about having to unify, I've done that" in Atlanta during the 1988 Democratic National Convention where party divisions sealed after a sometimes brutal battle between Jackson and presidential candidate Michael Dukakis.

Randy Horiuchi, Utah's Democratic chairman, said Wiener gave a lot of support to Utah's party when he served as chairman of the Association of State Democratic Chairmen. Wiener understands the concerns of Western states, Horiuchi said.

"Four years ago we were at our lowest point in our party's history. Rick Wiener decided . . . that if Democrats could win in Utah, they could win anywhere," Horiuchi said. "He took us under his wing, pushed us, excited us and helped us with human and financial support."

Wiener said he is a proven campaigner who can help party candidates win elections and who can help Democrats regain the White House in 1992.

"We believe that the job of the Democratic Party is winning elections," he said. "Without winning elections, we don't have the opportunity to implement our ideals. All we're doing at that point is just talking to each other."

But Brown said winning elections requires an identifiable perception of the party.

"We haven't been able to come up with that clear, concise, easily conceivable point of view" of the party, he said.

"I think we're the party that has to listen. We are the one institution in this country that has to deal with race, religion and ethnicity" because of the diversity of its members, said Brown. "The last thing that this country needs is two Republican parties."

The men were on the fourth of a five-city tour before the Feb. 10 vote to decide who will succeed outgoing DNC Chairman Paul Kirk.