In Washington, Sen. Rudy Boschwitz (R-Minn.) is known as a highly skilled political fund-raiser and loyal supporter of President Reagan who favors increased defense spending and opposes a nuclear-weapons freeze.

Here in Minnesota, he is known as good old Rudy, a somewhat quirky millionaire who wears red plaid lumberjack shirts, sells root beer-flavored milk at the state fair, tells people to have a nice day and frequently turns up at professional wrestling matches and polka dances to drum up support for his reelection.

Since early this year, he has also bombarded the state with slick television commercials showing himself as the state's consummate problem-solver. In one, a weathered Scandinavian farmer who credits the first-term senator with helping to lessen his tax burden looks into the camera and says, "I just want to say tanks, Rudy."

Minnesotans relish politicians who are folksy and slightly offbeat. And Boschwitz, 53, a German immigrant who first made a name with TV commercials pushing his Plywood Minnesota products, is riding the crest of extraordinary popularity.

Despite a voting record not always in tune with a state that overwhelmingly supports a nuclear freeze, many knowledgeable Republicans and members of the Democratic-Farmer-Labor Party say they believe that Boschwitz is unbeatable this year. He is running 19 to 22 points ahead of DFL Party challenger Joan Anderson Growe in the latest polls and is outspending her by better than 5 to 1 for crucial television, radio and newspaper advertising.

Even Growe's most important backer, Gov. Rudy Perpich, a maverick DFL member whose popularity rivals Boschwitz's, has said he likes Boschwitz too much to say anything nasty about him publicly.

"The truth is, Joan Growe is going down in flames and Rudy doesn't want to burn any bridges," a close aide to the governor explained.

Growe also appears to be struggling against a rising conservative tide that has left the once-powerful DFL Party demoralized and confused and could well result in a Reagan victory over Walter F. Mondale in the latter's home state next month.

"The politics of Minnesota's late senator Hubert Humphrey are dead, and even Humphrey at the end couldn't put it together himself," said one high-ranking DFL official. "How are they Mondale and Growe going to do it? I mean, if the master himself couldn't do it, how are they going to do it?"

Growe, 49, a three-term secretary of state and a former member of the state legislature, acknowledges she trails badly. She contends that Boschwitz is using his $5 million campaign war chest to lull voters to sleep and his happy-talk campaign to obscure his voting record.

Boschwitz concedes that rural areas have not benefited from the recovery in Minnesota's economy, but says he has done everything he could to help farmers. A member of the Senate Agriculture Committee, he helped broker compromise dairy-price legislation last December to reduce excess production.

But Jim Nichols, Minnesota commissioner of agriculture, argues that the program will force 5,000 Minnesota dairy farms out of business. Said Nichols: "With friends like Boschwitz, who needs enemies?"

Growe recently began running TV ads blasting Boschwitz for failing to debate her until now and for failing to release his income-tax returns, which she said probably would show that Boschwitz benefited personally from tax-law changes for which he voted as senator.

"He follows Reagan on everything else. I don't know why he doesn't follow him on income taxes," Growe said last week while campaigning in northern Minneosta, a traditional DFL stronghold now up for grabs.

Last Thursday, Boschwitz offered to take part in three debates with Growe, but he steadfastly refused to release his tax returns because, he said, it would be an unwarranted invasion of his privacy.

Growe and her supporters say they still can pull off a victory if the DFL -- a party built by Humphrey, former governor Orville Freeman and Mondale -- shakes off its lethargy and turns out a massive vote. The key to this is a strong showing by Mondale, but so far little indicates that this will happen.

A Northstar Poll published Sept. 8 by the St. Paul Pioneer Press & Dispatch and WCCO-TV showed Reagan leading Mondale 47 percent to 40 percent among Minnesota voters, although those interviewed disagreed with Reagan's foreign policy and his opposition to a nuclear freeze and were split over his economic programs. A Washington Post-ABC News poll published last week also indicated a strong Reagan lead here.

The Northstar survey of 931 voters, conducted between Aug. 24 and Sept. 1, indicated that by 50 percent to 26 percent, Minnesotans feel they are better off today than four years ago. Among those who feel better off, six in 10 said they preferred Reagan to Mondale.

"Mondale doesn't project very well," Boschwitz said recently while in the Twin Cities area. "It's a matter of chemistry, and right now the issues aren't with him and the times are better. We've gone through a recovery with the exception that the recovery has not reached down to rural America.

"Minnesota is a relatively conservative state," he continued. "People in their own habits are conservative, and I think Ronald Reagan appeals to their morality and their standards."

Mondale's lackluster showing is hurting DFL campaigns besides Growe's. Political analysts here say the Republicans are threatening to wrest control of the Minnesota House of Representatives from the DFL, although the DFL is expected to retain control of the state Senate.

Conservative Republicans are mounting strong challenges to two first-term Democratic House members, Reps. Timothy J. Penny in the 1st District and Gerry E. Sikorski in the 6th District.

"We Republicans have a sense of the future, and the DFL, they don't know where they're going," said Frank Graves, a conservative Republican national committeeman from Minnesota. "They're grasping at straws."

In fact, the Boschwitz-Growe contest comes at a time of major upheaval and difficulties in both state parties.

The DFL organization is exhausted and divided after years of internal feuding over the abortion issue. At the party's state convention in June, pro- and anti-abortion forces slugged it out for 26 straight hours before Growe, a feminist, won the Senate endorsement on the 19th ballot.

Perpich also is giving the party fits. After a term as governor from 1977 to 1979, he returned from an overseas job two years ago and bumped off Warren Spannaus, the DFL-endorsed candidate for governor, in the primary election and went on to win the general election.

Since then, Perpich has maintained cool relations with party officials. Many speculate that Perpich will neither seek nor accept his party's endorsement if he seeks another term in 1986.

Mary Monahan, the state DFL chairman, said "it would be just awful" and embarrassing for the party if Perpich turned down the endorsement.

But the Minnesota Independent-Republican Party has its own problems. An influx of conservative fundamentalist Christians in recent years has altered the party's makeup and priorities dramatically, alarming its more moderate members.

With the religious right in firm control, the party's state convention in June adopted a platform that supports prayer in schools, opposes abortion and the Equal Rights Amendment and advocates teaching both the evolution and creation theories. It also blocked two high-ranking female party officials from going to the national convention as delegates because of their moderate views.

Boschwitz appears to have made peace with the religious right, while the state's other senator, David F. Durenberger (R), has expressed concern about the narrow focus of the religious right.

"Now that they're involved in politics, maybe they'll discover there's more to it than just abortion," Durenberger said recently. "The problem is, if they stay dominant, how do you attract others in without having a bloodbath?"

Marsie Leier, head of the Reagan-Bush campaign in Minnesota, and Rep. Vin Weber (R-Minn.), both close allies of the religious right, said the infusion of these supporters actually would strengthen the party.

"I continue to believe that element within our party is going to end up being a substantial plus for us," Weber said. "They're not the evil force they're being portrayed as."