Scott Matheson isn't a household word in American politics, but in the history of the 1980 elections, he deserves at least a footnote.

He is a Democrat from Utah, and as Ronald Reagan was sweeping his state with 73 percent of the vote--the highest percentage in the nation -- Matheson was busy winning reelection as governor by an 11-point margin.

As the broken-down Democratic Party begins its rebuilding job, many of its leaders are looking West, and lots of them are listening to Matheson.

"The national Democratic Party has adopted a policy that hasn't helped anybody, including the West," he says. "They have ignored the basic political attitudes of the country and let the extremes come in. The national Democratic Party has isolated itself from the average Democratic candidate -- and the average voter. In several western states, I think the Democratic Party is on the ropes."

If the party organizations "don't get their act together and regroup in time for the 1982 elections, then we are in real trouble," he warns.

This is not mere rhetoric. Matheson is describing a battle for America's new political heartland, one that the Democrats begin at an enormous disadvantage.

This fight, no matter who wins, will have profound implications for the future of American politics. If the Democrats lose it, the Republicans will have locked up the booming West, forcing the Democrats to adopt an enclave strategy of protecting their base in the declining Northeast and Midwest.

If the Democrats win it, they will have done so by adapting to new political realities and to an ethic that is largely alien to the New Deal philosophy that guided them successfully for almost half a century.

The Democrats' problem is apparent from the vote last November--and what has happened since. In the 14 states of the greater West (the Rockies, the Pacific Coast, and Oklahoma and Texas), former president Carter attracted 40 percent of the vote or more only in Texas, and even there he lost by 15 points. Today, the West is the only region where more people identify themselves as Republicans than Democrats. According to a June Washington Post/ABC News poll, Democrats outnumbered Republicans 37 percent to 24 percent nationally. The West was 27 percent Democrat and 29 percent Republican.

But the problems facing the Democrats are more serious than the results of just one election. The West has voted solidly Republican in every presidential election since 1948, with the exception of the Johnson landslide in 1964. And it is now the center of New Right strength in the U.S. Senate.

For years, Democrats have either ignored the West or inflamed it. Carter angered the West with insensitive water policies, an MX basing system that would have torn up Nevada and Utah, and other seemingly antiwestern policies. But Carter wasn't alone.

"The national party has been pushing a program that went out 10 years ago," says Montana Gov. Ted Schwinden, who like Matheson bucked the Reagan tide last November to win election.

"The average westerner," says Arizona's Democratic Gov. Bruce Babbitt, "would say the Democratic Party . . . has gotten short on ideas, that it has tended to approach every problem with a blank check from the federal government and that it has become insensitive to regional issues and state and local issues. That is going to have to be changed."

In appealing for the support of special interests, the Democrats lost their appeal to many westerners, Babbitt says.

"Westerners feel good about themselves," Babbitt added in an interview. "They are reasonably progressive people, they are activists, oriented to the future and they want to get on to pragmatic problem solving. The Democratic Party at the national level is perceived by westerners as being just a little bit out of touch with reality."

Two decades ago, the Democratic Party could afford to write off the West, which, with the exception of California, had the power neither to swing an election nor to set the national agenda. That has changed.

"We've always known the prevailing winds are from the West," says Nevada's Republican Gov. Robert List. "So now are the political winds."

The 1980 census confirms this. Together, these 14 states grew by 24.3 percent.

While steel and automobile factories in the old industrial heartland of the Northeast and Midwest shut their doors, workers headed to the job-rich Southwest and West, whose booming economies were fueled by a trio of expanding industries: energy, electronics and defense.

So far, the Republicans have exploited the political potential of this phenomenon better than the Democrats. The idea of former California governor Ronald Reagan, with the aid of ex-Texas oilman--and transplanted Yankee--George Bush, undoing the New Deal of Franklin Delano Roosevelt, a former New York governor, is a striking political parallel to the shift in population and economic power from East to West.

That trend will continue. Reagan's arms buildup means billions of dollars for the defense and aerospace companies of the West. Demands for domestic energy supplies will keep oil and coal companies drilling and mining in Texas, Oklahoma and the Rockies. And the Census Bureau predicts a continuing shift of population into the West for the rest of the century, spurred not only by the economic opportunities of this high-growth area, but by a birth rate far above the national average.

What this means is that the Democrats cannot afford to chart their futures without taking the West into consideration, as the new leadership at the Democratic National Committee is painfully aware.

"The West is a very important part of our rebuilding plans," says Eugene Eidenberg, director of the DNC. "The assumption that the Democratic Party has lost the West is both wrong in fact and would be a catastrophe if true."

If there is a home for Democrats out West, it will look much different than the house that Roosevelt built.

"We do not have out here the traditional mainstays of the Democratic Party," Arizona's Babbitt says. "The union movement is weak, the minority population is relatively low, and you don't have that intellectual establishment that has been a mainstay of the party." Nor does the West have the kind of big-city machines that once helped bind voters to the Democrats.

This phenomenon helps explain why a massive demonstration such as that Saturday in Washington has relatively little bearing on the political fight out here over the future of the party. Solidarity Day's chief organizers--labor leaders with help from the black civil rights movement and others--represent groups with little clout in the West. They are among the "special interests" that many Westerners believe already have too much influence on the Democratic Party.

The most important political fact about minorities in this new heartland is that they are predominantly Hispanics, not blacks. Many are recent immigrants from Mexico who are ineligible to vote. Many of those who do vote are attracted to the Republican gospel of economic development and a strong defense. According to some postelection surveys, Reagan got 30 percent of the Hispanic vote last year.

Where the Democratic Party has flourished in the West--and in many states they still hold an edge in registration--there is now discord. The New Mexico House is controlled by a coalition of Republicans and conservative Democrats.

Says Speaker C. Gene Samberson, a Democrat, "The Democratic Party, at least for many, many years, was broad enough and big enough to have all kinds of philosophies in it. It was only during the last several years that those in control seemed to be intent on pushing out the conservative philosophy. I think the party leadership has realized that an error was made . . . but they have a long way to go."

The Texas Democratic Party is struggling with boll weevils in Congress and a statehouse alliance between Republicans and conservative Democrats that drew a redistricting plan favorable to the GOP.

One hope for the Democrats is the independent spirit and latent populism that exists in the West, where there is distrust not only of big government, but big banks, eastern corporations and others who have for years extracted the mineral riches of the West with little regard for the people. This is, after all, the region that spawned the Industrial Workers of the World, the Wobblies.

"All of the evidence is actually that this is an independent region that looks at personalities more than parties," says Colorado's Gov. Dick Lamm.

That means, according to Lamm, that the power of the New Right in the West ultimately will hurt the Republicans. "The Republican Party in the West has pretty much been captured by the far right and has abondoned the middle to us," he says.

Democrats also believe that the policies of Interior Secretary James G. Watt will create a western backlash against Reagan and the Republicans. "Jim Watt is the krypton around the necks of the Reagan administration and the Republicans," says the Democratic pollster Peter D. Hart.

But so far, Watt is popular among most western governors, regardless of party. While he has angered environmental groups, many westerners support his policies. Watt simply hasn't done enough yet to make most people aware of him.

A Washington Post poll earlier this year showed that while 31 percent of the people in the District area had an opinion about Watt, only 18 percent of the public nationwide had one. Watt has been careful to consult western governors on issues of water rights, mineral leasing and land policy.

What gives national Democratic leaders the most hope about the West, however, is the belated recognition that it is the region with the greatest concentration of Democratic governors. Of eight states in the Rocky Mountains, Democrats control the governorships in seven. Only Nevada's governorship has escaped them.

In addition to Matheson, Babbitt and Lamm, the others are Ted Schwinden of Montana, John V. Evans of Idaho, Ed Herschler of Wyoming and Bruce King of New Mexico.

How have they managed to win in this hostile environment?

"We share a western ethic," says Montana's Schwinden, who challenged an incumbent Democrat in 1980, won the primary and went on to win the general election by 10 percentage points. "Democrats out West are people-oriented, they're active, outspoken, articulate. They're doers, not philosophical ideologues."

"In state races, you get a different breed of cat," says Nevada's List. "Western Democrats are more conservative. Many of them are philosophically almost indistinguishable from their Republican counterparts."

The Democratic National Committee, under new chairman Charles T. Manatt, has begun to pay more attention to such "remarkable resources" as Lamm, Babbitt, Matheson and California Gov. Edmund G. (Jerry) Brown, recently elected as the leader of the Democratic governors.

Manatt has traveled to western states this year, has hired a western field director and will set up a governors' desk at the DNC to help in the rebuilding of the state party organizations and in the 1982 elections. He also made a symbolic point by taking his first meeting as DNC chairman to Denver last spring.

"The Democratic Party in the West has not had nearly the care and feeding it should," Manatt says.

But in the organizational battle, the Republicans still look stronger. A survey of the Western states shows state Republican parties outraising Democrats by huge margins.

In California, Democrats raised $180,000 as of July 1. Republicans, as of July 31, had raised $1.4 million. In New Mexico, the Republican advantage was $90,000 to $10,600.

In addition, Republican state parties are far better staffed. Nevada's Democratic Party has one "full-time volunteer." In Idaho, the party's executive director is only now being paid a living wage.

This could begin to tell next fall, in the race for Congress and more importantly in the races for governor. Thirty-six gubernatorial seats are up in 1982, including 11 in the West.

Rewpublicans are gearing up for those Democrat-held seats as never before. The Republican Governors' Association in Washington hopes to raise $1 million for races this fall and is conducting candidate schools for incumbents and challengers alike. "We've never done anything like this on such a grand scale," says John Stevens, RGA executive director.

All of this has stirred up the Democratic Party activists in the West. As a result, the 1982 western governors' races--which will turn on state issues and the records of the incumbents--may present less of a problem than the national elections in 1984 and beyond.

The more serious problem facing Democrats is developing a set of ideas appealing to the West and then nominating candidates who can run with them.

"I'll debate any Republican in my state on state issues," Lamm says. But on national issues? "That's were you lose."

"The Democratic Party can't forget the West," says Wyoming's Herschler. "We're still part of the union out here. You have to be a party of the whole country."

Republicans and Democrats alike concede that population shifts have made the West potentially more volatile than ever before.

"The important thing to remember about immigrants is that they are socially and politically very fluid," says Babbitt. "They are pragmatic and open-minded people. On every issue, public opinion is up for grab."