Primaries in 8 States Set Fall Battleground : Politics: From the statehouses to Capitol Hill, few incumbents face tough challenges. But November lineups will find GOP fighting for House control.

On a busy primary day across the nation Tuesday, South Dakota Gov. Walter D. Miller was defeated, while the governors of Iowa and Alabama survived primaries.

Republicans picked New Jersey’s Assembly speaker to challenge Democratic Sen. Frank R. Lautenberg, and a former Pentagon official to challenge Democratic Sen. Jeff Bingaman in New Mexico. Also, freshman Rep. Michael Huffington easily won the GOP nomination to challenge Democratic Sen. Dianne Feinstein of California.

There was voting in eight states in all, and lineups for more than 80 House races were being set. But only a few House incumbents faced significant primary challenges.

South Dakota’s Miller, one of five governors who faced a primary challenge Tuesday, was defeated by former GOP Gov. Bill Janklow, 54% to 46%. Janklow served as governor from 1979 to 1986. South Dakota Democrats nominated former Dakota Wesleyan University President Jim Beddow.

In California, Republican Pete Wilson won easily but still faced protest votes from conservatives who supported his little-known opponent, high-tech executive Ron Unz.

New Mexico Democratic Gov. Bruce King was surviving a tough challenge from Lt. Gov. Casey Luna in his bid for a fourth, non-consecutive term in November. With 86% of the vote counted, King had 39% to 36% for Luna. The Republican race was too close to call early today.

In Iowa, three-term Gov. Terry E. Branstad got a scare but defeated moderate GOP Rep. Fred Grandy, the former “Love Boat” actor, by a margin of 52% to 48%. Branstad will face state Atty. Gen. Bonnie Campbell, who easily won her Democratic primary.

Alabama Democratic Gov. Jim Folsom won the right to seek a full term by defeating Paul Hubbert, a teacher’s union leader and the party’s 1990 gubernatorial nominee. Folsom was lieutenant governor and moved up last year when GOP Gov. Guy Hunt was removed from office because of a conviction on ethics charges. Republicans face a June 28 runoff, with former Democratic Gov. Fob James one of the two GOP candidates.

Republicans need to gain seven seats to control the Senate for the first time since 1986, a daunting but not impossible task given recent Democratic setbacks and the high number of competitive contests.

Of five Senate primaries Tuesday, three figured prominently in the GOP’s hopes: New Jersey, New Mexico and California.

In New Jersey, Lautenberg easily defeated two primary opponents, but he is considered among the weakest Democratic incumbents this fall. State Assembly Speaker Chuck Haytaian coasted to victory in the GOP primary and immediately took aim at Lautenberg as a big-spending liberal who has lost touch with New Jersey voters.

Bingaman was unopposed in the New Mexico primary. He will face former Undersecretary of Defense Colin McMillan, who routed two opponents to win New Mexico’s Republican nomination. Bingaman is favored, but Republicans hope to make his support of President Clinton’s budget plan--and its tax increases--an issue.

Also on the GOP’s target list is Feinstein of California, who defeated two token opponents Tuesday.

Mississippi GOP Sen. Trent Lott cruised to victory over two little-known challengers and is heavily favored to win a second term in November. Two Democrats will face off in a June 28 runoff for the right to oppose Lott.

Montana also had a Senate primary. GOP Sen. Conrad Burns was unopposed. In the Democratic race, attorney Jack Mudd easily beat former Sen. John Melcher, who lost the seat to Burns in 1988.