REGIONAL REPORT / MIDWEST POLITICS : Opposition to Rising Taxes Could Cost GOP 2 Governorships : The party is in trouble in Nebraska and Kansas. Campaigning is turning nasty in normally well-behaved Minnesota.

Furor over rising taxes could cost Republicans at least two governorships in the Midwest, and active campaigning by President Bush, whose own popularity has taken a nose dive in the midst of budget woes in Washington, may not be able to help.

Even though Republicans appear to be in a good position to capture the governor’s office in Ohio and retain it in Wisconsin, Iowa and possibly Illinois, GOP governors in Kansas and Nebraska are in trouble.

The tone of campaigning in the Midwest has turned nasty. Negative personality-based campaigning has cropped up in a number of important races. In normally well-behaved Minnesota, for example, one gubernatorial candidate’s campaign has been seriously threatened by allegations that the candidate had once tried to get two teen-age girls to swim nude with him.

Here is a look at some of the major races:

Illinois

Democrats thought they had a good chance of regaining the governor’s office because Republican Gov. James R. Thompson is not seeking reelection. But Democrat Neil Hartigan is running neck and neck with Republican Jim Edgar, who is lagging only slightly in the polls.

Hartigan has campaigned against taxes, promising to increase funding for education through budget cuts elsewhere instead of extending a two-year, 20% state income surtax adopted in 1989 to help improve Illinois’ schools. He has also sought repeatedly to link Edgar to Thompson, who raised taxes 25 times during his 14-year tenure in office.

But a similar attempt by Republican Rep. Lynn Martin to link liberal Democratic Sen. Paul Simon to higher taxes appears to have failed. Simon holds a wide lead in the opinion surveys as he seeks reelection.

Minnesota

In what is being called one of the dirtiest Minnesota campaigns in memory, Democratic-Farmer-Labor Party Gov. Rudy Perpich, seeking an unprecedented fourth term, is facing Independent-Republican challenger Jon Grunseth, a 44-year-old businessman who has not held public office, and State Auditor Arne Carlson, who lost to Grunseth in the primaries but this week announced that he will be a write-in candidate.

Carlson reentered the race after a scandal enveloped Grunseth. Two women alleged in sworn statements that, when they were 13 and 14 years old, Grunseth tried to get them to take off their bathing suits to join him for a nude swim at a party at his home. Grunseth has rejected suggestions that he withdraw from the race.

He countered the allegations by releasing affidavits from 16 people who attended the party saying the charges are false, and he also took a polygraph test, which he said shows him to be innocent of the charges.

Perpich had been considered vulnerable at the start of the campaign. At the Democratic-Farm-Labor Party convention in June, it took the governor, whose anti-abortion stance runs counter to the party’s position, four ballots to win the party endorsement. But Grunseth’s troubles have boosted his stock considerably.

In the Senate race, Republican incumbent Rudy Boschwitz has apparently been hurt by the budget debacle in Washington. A Minneapolis Star-Tribune/KSTP-TV poll Wednesday showed him leading Democratic challenger Paul Wellstone by only 48% to 45%.

Nebraska

Republican Gov. Kay A. Orr is in an uphill battle for reelection after announcing her support for a proposed nuclear waste dump in the state and proposing a tax increase despite a no-new-taxes campaign four years ago. President Bush has made three campaign swings in her behalf, but she still trails Democrat Ben Nelson in the polls.

The planned dump has raised tempers so high in Boyd County in northeastern Nebraska that Orr won’t campaign there because of threats on her life. The Boyd County Republican Party endorsed Nelson over Orr, the nation’s first Republican woman elected governor, because of the nuclear dump.

A lackluster Senate race heated up recently when former Texas Sen. John Tower, campaigning for Republican Hal Daub, said he had heard rumors that Daub’s opponent, Democratic incumbent J. James Exon, drank excessively.

Exon had helped lead opposition to Tower’s nomination as defense secretary, in which Tower’s drinking became an issue. The allegation about Exon has led to calls for the release of Exon’s medical records and unleashed retaliatory innuendo about Daub’s family life.

Ohio

The former Republican mayor of Cleveland, George V. Voinovich, is running a strong race for governor against Democrat Anthony J. Celebrezze, the Ohio attorney general.

Voinovich has benefited from the economic rebound of Cleveland, which was on the brink of bankruptcy when he took office in 1979. Celebrezze does not appear to have helped his cause by reversing his longstanding opposition to abortion on the eve of his campaign, although his own polls now show him building a slim lead in the race.

Ohioans will also vote on a constitutional amendment to legalize casino gambling. The proposal authorizes a casino in economically devastated Lorain as a pilot project but eventually could permit up to seven casino resort districts throughout the state if local voters approve.

Michigan

Democratic Gov. James J. Blanchard appears unscathed by negative publicity last month after he dumped Lt. Gov. Martha Griffiths as his running mate in favor of a younger woman. He also seemed undamaged by his ex-wife’s book about their marriage in which she accused him of having had an extramarital affair with the woman who is now his second wife.

Blanchard is running well ahead of Republican challenger John Engler, the state Senate majority leader with whom he’s had an eight-year rivalry. Both are in the political mainstream, so many observers view the battle as a grudge match.

Wisconsin

The governor’s race is at least in part a referendum on the welfare reforms initiated by Republican Gov. Tommy G. Thompson. He leads Democrat Thomas A. Loftus, Speaker of the state Assembly, by 30 to 40 percentage points in the polls.

Among Thompson’s reforms is Learnfare, a program that reduces welfare payments to people who don’t keep their teen-agers in school. Loftus has criticized the program and Thompson’s opposition to abortion except in cases of rape, incest and to save a woman’s life. Loftus has tried to paint Thompson as the candidate of the rich and has criticized him for taking contributions from dog track interests.

Iowa

Democratic state House Speaker Don Avenson faces an uphill fight to unseat two-term incumbent Republican Gov. Terry E. Branstad. Avenson, 46, is seeking in his television commercials to cast Branstad as a protector of the wealthy. Branstad has been widening his lead in the polls but is only 13 percentage points ahead, according to a recent Des Moines Register poll. Abortion is an issue in the campaign, with Avenson drawing significant support from the National Abortion Rights League.

The Senate race between Democratic incumbent Tom Harkin and GOP challenger Rep. Tom Tauke is one of the hottest in the country. Harkin, who has been pounding out a populist call for increasing taxes on the rich, appears to have been helped by the budget crisis. In addition, Tauke, a firm opponent of abortion, is one of the chief targets of abortion rights groups.

Kansas

Republican Gov. Mike Hayden and his challenger, Democratic state Treasurer Joan Finney, are tied at 37% in the latest Topeka Capital-Journal poll. Voters, angered by a property tax overhaul that sent tax bills soaring, narrowly renominated Hayden in the Republican primary over an anti-tax challenger. But the latest poll showed Finney’s support weakening.